List of publications

Institute for Analysis and Numerics

Publications

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Submitted / Under Review

Published
Online First
  • Gonon L, Grohs P, Jentzen A, Kofler D, Šiška D. . ‘Uniform error estimates for artificial neural network approximations for heat equations.’ IMA Journal of Numerical Analysis . doi: 10.1093/imanum/drab027.
  • Hutzenthaler M, Jentzen A, Kruse T. . ‘Overcoming the curse of dimensionality in the numerical approximation of parabolic partial differential equations with gradient-dependent nonlinearities.’ Foundations of Computational Mathematics . doi: 10.1007/s10208-021-09514-y.
  • Cheridito P, Jentzen A, Rossmannek F. . ‘Efficient approximation of high-dimensional functions with neural networks.’ IEEE Transactions on Neural Networks and Learning Systems . doi: 10.1109/TNNLS.2021.3049719.
  • Jentzen A, Kuckuck B, Müller-Gronbach T, Yaroslavtseva L. . ‘Counterexamples to local Lipschitz and local Hölder continuity with respect to the initial values for additive noise driven SDEs with smooth drift coefficient functions with at most polynomially growing derivatives.’ Discrete Contin. Dyn. Syst. Ser. B tbd (early access version). doi: 10.3934/dcdsb.2021203.
  • Elbrächter D, Grohs P, Jentzen A, Schwab C. . ‘DNN Expression Rate Analysis of High-dimensional PDEs: Application to Option Pricing.’ Constr. Approx. . doi: 10.1007/s00365-021-09541-6.
  • Schlichting A, Seis C. . The Scharfetter-Gummel scheme for aggregation-diffusion equations.’ IMA J. Numer. Anal. 2021.
Accepted / In Press (Not yet published)
Submitted / Under Review

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Online First
  • Bansal H, Rave S, Iapichino L, Schilders WHA, van de Wouw N. . ‘Model order reduction framework for problems with moving discontinuities.’ Contributed to the Proceedings of ENUMATH 2019, Egmond aan Zee.
Accepted / In Press (Not yet published)
  • Beck C, Jentzen A, Kuckuck B. . ‘Full error analysis for the training of deep neural networks.’ Infin. Dimens. Anal. Quantum Probab. Relat. Top. tbd (to appear).
  • Crismale V, Friedrich M, Solombrino F. . ‘Integral representation for energies in linear elasticity with surface discontinuities.’ Adv. Calc. Var. 2020.
  • Friedrich M, Kruzik M, Stefanelli U. . ‘Equilibrium of immersed hyperelastic solids.’ DCDS-S 2020.
  • Friedrich M, Kruzik M, Valdman J. . Numerical approximation of von Kármán viscoelastic plates.’ DCDS-S 2020.
  • Altenbernd Mirco, Dreier Nils-Arne, Engwer Christian, Göddeke Dominik. . ‘Towards local-failure local-recovery in PDE frameworks: the case of linear solvers.’ Contributed to the HPCSE 2019, Ostrava, Czech Republic.
  • Rave S, Saak J. . A Non-stationary Thermal-Block Benchmark Model for Parametric Model Order Reduction.’ Contributed to the ENUMATH 2019, Graz.
  • Mlinarić P, Rave S, Saak J. . Parametric model order reduction using pyMOR.’ Contributed to the MODRED 2019, Graz.
Submitted / Under Review

Published
Online First
  • Riesselmann Johannes, Ketteler Jonas Wilhelm, Schedensack Mira, Balzani Daniel. . ‘Three‐field mixed finite element formulations for gradient elasticity at finite strains.’ GAMM-Mitteilungen xxx. doi: 10.1002/gamm.202000002.
  • Hellman Fredrik, Keil Tim, Målqvist Axel. . ‘Multiscale methods for perturbed diffusion problems.’ Oberwolfach Reports 2019.
Accepted / In Press (Not yet published)
Submitted / Under Review

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Accepted / In Press (Not yet published)

Published
Online First
  • Grebhahn A, Engwer C, Bolten M, Apel S. . ‘Variability of Stencil Computations for Porous Media.’ Concurrency and Computation: Practice and Experience Special Issue on Advanced Stencil-Code Engineering.
  • Engwer C, Falgout R, Yang UM. . ‘A Framework of Stencil Computations for PDE based Applications with Examples from DUNE and hypre.’ Concurrency and Computation: Practice and Experience Special Issue on Advanced Stencil-Code Engineering.
Accepted / In Press (Not yet published)
Submitted / Under Review
  • Buhr Andreas, Smetana Kathrin. . Randomized Local Model Order Reduction : arXiv:1706.09179, .
  • Burger M, DiFrancesco M, Fagioli S, Stevens A. . ‘Sorting phenomena in a mathematical model for two mutually attracting/repelling species.’ SIAM J. Math. Analysis 2017.

Published
Online First
Submitted / Under Review
  • Hefter M, Jentzen A, Kurniawan R. . Weak convergence rates for numerical approximations of stochastic partial differential equations with nonlinear diffusion coefficients in UMD Banach spaces.’ arXiv .
  • Brinkmann Eva-Maria, Burger Martin, Rasch Julian, Sutour Camille. . ‘Bias-Reduction in Variational Regularization.’ Journal of Mathematical Imaging and Vision Special Issue MIA 2016.
  • Engwer C, Henning P, M\ralqvist A, Peterseim D. . Efficient implementation of the Localized Orthogonal Decomposition method arXiv, .
  • Lehrenfeld C, Reusken A. . L2-estimates for a high order unfitted finite element method for elliptic interface problems : arXiv eprints, .
  • Lehrenfeld C, Reusken A. . ‘Analysis of a high order unfitted finite element method for elliptic interface problems.’ arXiv preprint arXiv:1602.02970 1602.02970.

Published
Online First
Accepted / In Press (Not yet published)
  • Burger M, Dirks H, Frerking L. . ‘On Optical Flow Models for Variational Motion Estimation.’ Radon Book Series 2016.
  • Engwer C, Gräser C, Müthing S, Sander O. . The interface for functions in the dune-functions module arXiv, .
  • Barchiesi M, Brancolini A, Julin V. . ‘Sharp dimension free quantitative estimates for the Gaussian isoperimetric inequality.’ Annals of Probability 2015.
Submitted / Under Review

Published
Accepted / In Press (Not yet published)
  • Sawatzky A, Xu Q, Schirra C, Anastasio M. . ‘Proximal ADMM for Multi-Channel Image Reconstruction in Spectral X-ray CT.’ IEEE Transactions on Medical Imaging -.
  • Sawatzky A. . ‘Performance of First-Order Algorithms for TV Penalized Weighted Least-Squares Denoising Problem.’ Contributed to the ICISP 2014, Cherbourg, Normandy, France.
Submitted / Under Review

Published
Online First
  • Hegemann Jan, Cantarero Alejandro, Richardson Casey L, Teran Joseph M. . ‘An explicit update scheme for inverse parameter and interface estimation of piecewise constant coefficients in linear elliptic PDEs.’ SIAM Journal on Scientific Computing 35.

Published
Online First
  • Kelkel J, Surulescu C. . ‘A multiscale approach to cell migration in tissue networks.’ Mathematical Models and Methods in the Applied Sciences 22, No. 3.
Accepted / In Press (Not yet published)
  • Gigengack F, Ruthotto L, Modersitzki J, Burger M, Wolters C, Jiang X, Schäfers K. . ‘A simplified pipeline for motion correction in dual gated cardiac PET.’ Contributed to the Bildverarbeitung für die Medizin, Berlin.

Published
Submitted / Under Review
  • Märkl C, Surulescu C. . Mathematical analysis and numerical simulations for a system modeling acid-mediated tumor cell invasion , .
  • Winkel C, Neumann S, Surulescu C, Scheurich P. . A minimal mathematical model for the dynamics of (TNF-) receptor signaling , .
  • Meral G., Surulescu C. . Mathematical modeling, analysis and numerical simulations for the influence of heat shock proteins on tumor invasion , .

Published
Accepted / In Press (Not yet published)
  • Engwer C, Bastian P, Kuttanikkad SP. . ‘An Unfitted Discontinuous Galerkin Finite Element Method for Pore Scale Simulations.’ In 9th International Workshop on State-of-the-Art in Scientific and Parallel Computing.: Springer.

  • Sawatzky A, Brune C, Wübbeling F, Kösters T, Schäfers K, Burger M. . ‘Accurate EM-TV algorithm in PET with low SNR.’ Contributed to the IEEE NSS/MIC 2008, Dresden, Deutschland. doi: 10.1109/NSSMIC.2008.4774392.
  • Schlake B. . Mathematical Models for Pedestrian Motion.
  • Busby M, Blum C, Tibben M, Fibikar S, Calzaferri G, Subramaniam V, De Cola L. . ‘Time, space, and spectrally resolved studies on J-aggregate interactions in zeolite L nanochannels.’ Journal of the American Chemical Society 130, No. 33: 10970-10976. doi: 10.1021/ja801178p.
  • Brune C, Maurer H, Wagner M. . „aaa Kantenerkennung im optischen Fluss als mehrdimensionales Steuerungsproblem.“. BTU Cottbus.
  • Dawood M, Kösters T, Fieseler M, Büther F, Jiang X, Wübbeling F, Schäfers KP. . ‘Motion correction in respiratory gated cardiac PET/CT using multi-scale optical flow.’. doi: 10.1007/978-3-540-85990-1_19.
  • Dawood M, Kösters T, Fieseler M, Büther F, Jiang X, Wübbeling F, Schäfers K. . ‘Multi-scale optical flow for respiratory motion correction in cardiac PET/CT.’ Contributed to the MICCAI, New York.
  • Surulescu C. . ‘On the Time-Dependent Motion of a Viscous Incompressible Fluid Through a Tube with Compliant Walls.’ Studia UBB Mathem LIII: 77-95.
  • Burger M, Pinnau R. . ‘A Globally Covergent Gummel Map for Optimal Dopant Profiling.’ Math. Models Meth. Appl. Sci. 19.
  • Burger M. . ‘A note on sparse reconstruction methods.’ In J Phys Conference Series, edited by Uhlmann G, 012002.
  • Burger M, Dolak-Struss Y, Schmeiser C. . ‘Asymptotic analysis of an advection-dominated chemotaxis model in multiple spatial dimensions.’ Commun. Math. Sci. 6: 1-28.
  • Burger M, Landa Y, Tanushev N, Tsai R. . ‘Discovering point sources in unknown environments.’ Contributed to the WAFR 2008.
  • Burger M. . ‘Finite element approximation of elliptic partial differential equations on implicit surfaces.’ Comp. Vis. Sci. .
  • Burger M, Stöcker C, Voigt A. . ‘Finite element based level set methods for higher order flows.’ J. Sci. Comp. 35: 77-98.
  • Burger M, Di Francesco M. . ‘Large time behavior of nonlocal aggregation models with nonlinear diffusion.’ Networks and Heterogeneous Media 3: 749-785.
  • Burger M, Pinnau R, Wolfram M. . ‘On-/Off-State design of semiconductor doping profiles.’ Commun. Math. Sci. 6: 1021-1041.
  • Favaro P, Soatto S, Burger M, Osher S. . ‘Shape from Defocus via Diffusion.’ IEEE Transactions PAMI 30: 518-531.
  • Burger M, Chu S, Markowich P, Schönlieb C. . ‘The Willmore functional and instabilities in the Cahn-Hilliard equation.’ Commun. Math. Sci. 6: 309-329.
  • Benning M, Kösters T, Wübbeling F, Schäfers K, Burger M. . ‘A Nonlinear Variational Method for Improved Quantification of Myocardial Blood Flow Using Dynamic H215O PET.’ Contributed to the IEEE NSS/MIC 2008, Dresden.
  • Burger M, He L, Markowich P, Schönlieb C. . ‘A generalization of Cahn-Hilliard inpainting for gray-value images.’ In PAMM Special Issue: ICIAM 07, 1041905-1041906.
  • Burger M, Chu S, Markowich P, Schönlieb C. . ‘Cahn-Hilliard inpainting and the Willmore functional.’ In PAMM Special Issue: ICIAM 07, 1011209-1011210.
  • Arning K, Burger M, Eisenberg B, Engl H, He L. . ‘Inverse problems related to ion channels.’ In PAMM Special Issue: ICIAM 07, 1120801-1120802.
  • Bastian P, Blatt M, Dedner A, Engwer C, Rober Klöfkorn, Kornhuber R, Ohlberger M, Sander O. . ‘A Generic Grid Interface for Parallel and Adaptive Scientific Computing. Part {II}: Implementation and Tests in {DUNE}.’ Computing 82, No. 2--3: 121-138. doi: 10.1007/s00607-008-0004-9.
  • Bastian P, Blatt M, Dedner A, Engwer C, Klöfkorn R, Ohlberger M, Sander O. . ‘A Generic Grid Interface for Parallel and Adaptive Scientific Computing. Part I: Abstract framework.’ Computing 82, No. 2--3: 103-119. doi: 10.1007/s00607-008-0003-x.
  • Bastian P, Chavarria-Krauser A, Engwer C, Jäger W, Marnach S, Ptashnyk M. . ‘Modelling in vitro growth of dense root networks.’ Journal of Theoretical Biology 254, No. 1: 99-109. doi: 10.1016/j.jtbi.2008.04.014.
  • Bastian P, Bauer J, Chavarria-Krauser A, Engwer C, Jager W, Marnach S, Ptashnyk M, Wetterauer B. . ‘Modeling and Simulation of Hairy Root Growth.’ In Mathematics-Key Technology for the Future: Joint Projects Between Universities and Industry 2004-2007, edited by Krebs H, Jäger W, 101-115. Springer Verlag. doi: 10.1007/978-3-540-77203-3_8.
  • Dreyer W, Herrmann M. . Numerical experiments on the modulation theory for the nonlinear atomic chain.’ Physica D: Nonlinear Phenomena 237, No. 2: 255-282. doi: 10.1016/j.physd.2007.09.003.
  • Henseler R, Herrmann M, Niethammer B, Velázquez JJL. . A kinetic model for grain growth.’ Kinetic and Related Models 1, No. 4: 591-617. doi: 10.3934/krm.2008.1.591.
  • Giannoulis J, Herrmann M, Mielke A. . Lagrangian and Hamiltonian two-scale reduction.’ Journal of Mathematical Physics 49, No. 10: 103505, 42. doi: 10.1063/1.2956487.
  • Goldsmith F, Ohlberger M, Schumacher J, Steinkamp K, Ziegler C. . ‘A non-isothermal PEM fuel cell model including two water transport mechanisms in the membrane.’ Journal of Fuel Cell Science and Technology 5, No. Journal of Fuel Cell Science and Technology: 5. doi: 10.1115/1.2822884.
  • Haasdonk B, Ohlberger M. . ‘Adaptive Basis Enrichment for the Reduced Basis Method Applied to Finite Volume Schemes.’ Contributed to the Finite Volumes for Complex Applications VI Problems & Perspectives: FVCA 6, Prague.
  • Klöfkorn R, Kröner D, Ohlberger M. . ‘Parallel adaptive simulation of PEM fuel cells.’ In Mathematics – Key Technology for the Future, edited by Krebs, Jäger, 235-249.
  • Haasdonk B, Ohlberger M. . ‘Reduced Basis Method for Finite Volume Approximations of Parametrized Linear Evolution Equations.’ M2AN Math. Model. Numer. Anal. 42, No. 2: 277-302. doi: 10.1051/m2an:2008001.
  • Dedner A, Ohlberger M. . A new $hp$-adaptive DG scheme for conservation laws based on error control.’ In Hyperbolic Problems: Theory, Numerics, Applications, edited by Benzoni-Gavage, Serre, 187--198. Berlin. doi: 10.1007/978-3-540-75712-2_15.
  • Haasdonk B, Ohlberger M, Rozza G. . ‘A reduced basis method for evolution schemes with parameter-dependent explicit operators.’ Electronic transactions on numerical analysis 32: 145--161.
  • Klöfkorn R, Kröner D, Ohlberger M. . Parallel and adaptive simulation of fuel cells in 3d.’ In Computational science and high performance computing III, 69--81. Berlin: Springer Verlag. doi: 10.1007/978-3-540-69010-8_7.
  • Wirth B, Sobey I. . ‘A model for an inverse power constitutive law for cerebral compliance.’ Mathematical Medicine and Biology 25: 113-131. doi: 10.1093/imammb/dqn006.
  • Stevens A, Velázquez JJL. . ‘Partial differential equations and non-diffusive structures.’ Nonlinearity 21, No. 12: T283-T289. doi: 10.1088/0951-7715/21/12/T04.

  • Sawatzky A. . Reflektoren in der Ultraschall-Tomographie.
  • Benning M, Lee E, Pao H, Yacoubou-Djima K. . Statistical Filtering of Global Illumination for Computer Graphics , .
  • Brune C. . Berechnung des optischen Flusses und Kantenerkennung mit Optimierungsmethoden.
  • Surulescu C. . ‘On the Stationary Interaction of a Navier-Stokes Fluid With an Elastic Tube Wall.’ Applicable Analyis 86: 149-165.
  • Schweizer B, Surovtsova I, Surulescu C. . ‘Fluid Flows and Free Boundaries.’ In Reactive Flows, Diffusion and Transport, edited by Jäger W, Rannacher R and Warnatz J.. Springer Verlag.
  • Surulescu C. . On the stationary interaction of a Navier-Stokes fluid with an elastic tube wall.’ Applicable Analysis 86, No. 2: 149--165. doi: 10.1080/00036810601108756.
  • Schweizer B, Bodea S, Surulescu C, Surovtsova I. . Fluid flows and free boundaries.’ In Reactive flows, diffusion and transport, 5--24. Berlin: Springer Verlag. doi: 10.1007/978-3-540-28396-6_1.
  • Kloeden PE, Jentzen A. . Pathwise convergent higher order numerical schemes for random ordinary differential equations.’ Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 463, No. 2087: 2929-2944. doi: 10.1098/rspa.2007.0055.
  • Ansini N, Babadjian J.F., Zeppieri C.I. . ‘The Neumann sieve problem and dimensional reduction: A multiscale approach.’ Mathematical Models and Methods in Applied Sciences 17, No. 5: 681-735. doi: 10.1142/S0218202507002078.
  • Braides A, Zeppieri C.I. . ‘A note on equi-integrability in dimension reduction problems.’ Calculus of Variations and Partial Differential Equations 29, No. 2: 231-238. doi: 10.1007/s00526-006-0065-6.
  • Burger M, Hausser F, Stöcker C, Voigt A. . ‘A level set approach to anisotropic flows with curvature regularization.’ J. Comp. Phys. 225: 183-205.
  • Burger M, Resmerita E, He L. . ‘Error estimation for Bregman iterations and inverse scale space methods.’ Computing 81: 109-135.
  • Burger M, Frick K, Osher S, Scherzer O. . ‘Inverse total variation flow.’ SIAM Multiscale Mod. Simul. 6: 366-395.
  • Ben Ameur H, Burger M, Hackl B. . ‘On some geometric inverse problems in linear elasticity.’ Math. Meth. Appl. Sci. 30: 625-647.
  • Burger M, Eisenberg B, Engl H. . ‘Inverse problems related to ion channel selectivity.’ SIAM J. Appl. Math. 67: 960-989.
  • Su B, Burger M. . Global weak solutions of non-isothermal front propagation problem.’ Electronic Research Announcements of the American Mathematical Society 13: 46--52 (electronic). doi: 10.1090/S1079-6762-07-00173-4.
  • Burger M, Capasso V, Micheletti A. . An extension of the Kolmogorov-Avrami formula to inhomogeneous birth-and-growth processes.’, edited by Aletti G, Burger M, Micheletti A, Morale D, 63--76. Berlin: Springer Verlag. doi: 10.1007/978-3-540-44446-6_6.
  • Haasdonk B, Ohlberger M. . ‘Basis Construction for Reduced Basis Methods by Adaptive Parameter Grids.’.
  • Fuhrmann J, Haasdonk B, Holzbecher E, Ohlberger M. . ‘Guest Editorial for Special Issue on Modelling and Simulation of PEM-FC.’ Journal of Fuel Cell Science and Technology 2007, No. Journal of Fuel Cell Science and Technology.
  • Klöfkorn R, Kröner D, Ohlberger M. . ‘Parallel and adaptive simulaiton of fuel cells in 3D.’.
  • Dedner A, Makridakis C, Ohlberger M. . ‘Error control for a class of Runge-Kutta discontinuous Galerkin methods for nonlinear conservation laws.’ SIAM J. Numer. Anal. 45: 514-538.
  • Ohlberger M, Schweizer B. . ‘Modelling of interfaces in unsaturated porous media.’ Discrete Contin. Dyn. Syst. , No. Dynamical Systems and Differential Equations. Proceedings of the 6th AIMSInternational Conference, suppl.: 794--803.
  • Henning P. . Die Heterogene Mehrskalenmethode f\�r elliptische Differentialgleichungen in perforierten Gebieten.
  • Rave S. . Über die Entscheidbarkeit gewisser Prädikate in der Theorie der C*-Algebren. Münster.
  • Fuhrmann J, Käs J, Stevens A. . ‘Initiation of cytoskeletal asymmetry for cell polarization and movement.’ Journal of Theoretical Biology 249, No. 2: 278-288. doi: 10.1016/j.jtbi.2007.08.013.

  • Lunkenheimer,P P, Redmann K, Kling N, Rothaus K, Jiang X, Cryer C, Wübbeling F, Niederer P, Heitz,U Ph, Ho,Y S, ,H R, erson,. . ‘The three-dimensional architecture of the left ventricular myocardium.’ The anatomical Record: Advances in Integrative Anatomy and Evolutionary Biology 288A, No. 6: 565-578.
  • Lunkenheimer PP, Redmann K, Kling N, Jiang XJ, Rothaus K, Cryer CW, Wubbeling F, Niederer P, Heitz PU, Ho SY, Anderson RH. . ‘Three-dimensional architecture of the left ventricular myocardium.’ Anatomical Record Part A: Discoveries in Molecular Cellular and Evolutionary Biology 288A, No. 6: 565-578. doi: 10.1002/ar.a.20326.
  • Surulescu, C. . ‘On the Stationary Motion of a Stokes Fluid in a Thick Elastic Tube: A 3D/3D Interaction Problem.’ AMUC 75: 95-106.
  • Surulescu C, Surulescu N. . ‘A Note on an Individual Bioequivalence Setting.’ J. Inequal. Pure Appl. Math. 7: 8.
  • Surulescu C, Surulescu N. . ‘A note on an individual bioequivalence setting.’ Journal of inequalities in pure and applied mathematics 7, No. 3: Article 100, 8 pp. (electronic).
  • Surulescu C. . ‘On the stationary motion of a Stokes fluid in a thick elastic tube: a 3D/3D interaction problem.’ Acta Mathematica Universitatis Comenianae 75, No. 1: 95--106.
  • Stainko R, Burger M. . ‘A one-shot approach to topology optimization with stress constraints.’ Contributed to the IUTAM Symposium on Topological Design Optimization of Structures, Machines, and Materials.
  • Burger M, Capasso V, Micheletti A. . ‘An extension of the Avrami-Kolmogorov formula to inhomogeneous birth-and-growth processes.’ Contributed to the Math Everywhere, Milano.
  • Berkels B, Burger M, Droske M, Nemitz O, Rumpf M. . ‘Cartoon extraction based on anisotropic image classification.’ Contributed to the Vision, Modeling, and Visualization Proceedings.
  • . Deterministic and Stochastic Modelling in Biomedicine, Economics, and Industry.
  • He L, Burger M, Osher S. . ‘Iterative total variation regularization with non-quadratic fidelity.’ J. Math. Imaging Vision 26: 167-184.
  • Burger M, Capasso V, Pizzocchero L. . ‘Mesoscale averaging of nucleation and growth processes.’ SIAM Multiscale Mod. Simul. 5: 564 - 592.
  • Burger M, Gilboa G, Osher S, Xu J. . ‘Nonlinear inverse scale space methods.’ Commun. Math. Sci. 4: 179-212.
  • Burger M, Capasso V, Morale D. . ‘On an aggregation model with long and short range interactions.’ Nonlinear Analysis: Real World Applications 8: 939-958.
  • Burger M, Hinze M, Pinnau R. . ‘Optimization models for semiconductor dopant profiling.’ In Transport Phenomena and Kinetic Theory: Applications to Gases, Semiconductors, Photons, and Biological Systems, edited by Cercignani C, Gabetta E, 91-116. Boston: Birkhäuser.
  • Burger M, Stainko R. . ‘Phase-field relaxation of topology optimization with local stress constraints,.’ SIAM J. Control. Optim. 45: 1447-1466.
  • Su B, Burger M. . Weak solutions of a polymer crystal growth model , .
  • Burger M. . ‘Surface diffusion including adatoms.’ Comm. Math. Sci. 4: 1-51.
  • Burger M, DiFrancesco M, Dolak-Struss Y. . ‘The Keller-Segel model for chemotaxis: linear vs. nonlinear diffusion.’ SIAM J. Math. Anal. 38: 1288-1315.
  • Burger M, Kaltenbacher B. . Regularizing Newton-Kaczmarz methods for nonlinear ill-posed problems.’ SIAM Journal on Numerical Analysis 44, No. 1: 153--182. doi: 10.1137/040613779.
  • Bastian P, Blatt M, Engwer C, Dedner A, Klöfkorn R, Kuttanikkad SP, Ohlberger M, Sander O. . ‘The Distributed and Unified Numerics Environment (DUNE).’ In Proc. of the 19th Symposium on Simulation Technique in Hannover, September 12 - 14.
  • Dreyer W, Herrmann M, Mielke A. . Micro-macro transition in the atomic chain via Whitham's modulation equation.’ Nonlinearity 19, No. 2: 471-500. doi: 10.1088/0951-7715/19/2/013.
  • Herrmann M, Naldzhieva M, Niethammer B. . On a thermodynamically consistent modification of the Becker-Döring equations.’ Physica D: Nonlinear Phenomena 222, No. 1-2: 116-130. doi: 10.1016/j.physd.2006.08.004.
  • Giannoulis J, Herrmann M, Mielke A. . Continuum descriptions for the dynamics in discrete lattices: derivation and justification.’ In Analysis, modeling and simulation of multiscale problems, edited by Mielke A, 435-466. Springer Verlag. doi: 10.1007/3-540-35657-6_16.
  • Dreyer W, Herrmann M, Rademacher JDM. . Wave trains, solitons and modulation theory in FPU chains.’ In Analysis, modeling and simulation of multiscale problems, edited by Mielke A, 467-500. Springer Verlag. doi: 10.1007/3-540-35657-6_17.
  • Burri A, Dedner A, Diehl D, Klöfkorn R, Ohlberger M. . ‘A general object oriented framework for discretizing nonlinear evolution equations.’, 93.
  • Burri A, Dedner A, Klöfkorn R, Ohlberger M. . ‘An efficient implementation of an adaptive and parallel grid in DUNE.’, 91.
  • Haasdonk B, Ohlberger M. . Reduced Basis Method for Finite Volume Approximations of Parametrized Evolution Equations , .
  • Ohlberger M, Vovelle J. . ‘Error estimate for the approximation of nonlinear conservation laws on bounded domains by the finite volume method.’ Math. Comp. 75: 113-150.
  • Brancolini A., Buttazzo G., Santambrogio F. . Path functionals over Wasserstein spaces.’ Journal of the European Mathematical Society 8, No. 3: 415-434.
  • Sobey I, Wirth B. . ‘Effect of nonlinear permeability in a spherical model of hydrocephalus.’ Mathematical Medicine and Biology 23: 339-361. doi: 10.1093/imammb/dql015.
  • Wirth B, Sobey I. . ‘An axisymmetric and fully 3D poroelastic model for the onset and treatment of hydrocephalus.’ Mathematical Medicine and Biology 23: 363-388. doi: 10.1093/imammb/dql014.
  • Dkhil F, Stevens A. . ‘Traveling wave speeds of nonlocally perturbed reaction diffusion equations.’ Asymptotic Analysis 46, No. 1: 81-91.
  • Hwang HJ, Kang K, Stevens A. . ‘Global existence of classical solutions for a hyperbolic chemotaxis model and its parabolic limit.’ Indiana University Mathematics Journal 55, No. 1: 289-316. doi: 10.1512/iumj.2006.55.2677.
  • DiBenedetto E, Perthame B, Stevens A (Eds.): . Mathematical biology. Abstracts from the workshop held May 1420, 2006. Organized by Emmanuele DiBenedetto, Benot Perthame and Angela Stevens. Oberwolfach Reports, Vol. 3, no. 2., S. 1385-1461. Zürich: European Mathematical Society. doi: 10.4171/OWR/2006/24.

Published
  • Natterer F, Wubbeling F. . ‘Marching schemes for inverse acoustic scattering problems.’ Numerische Mathematik 100, No. 4: 697-710. doi: 10.1007/s00211-004-0580-3.
  • Burger M. . ‘A model hierarchy for surface diffusion: the small slope case.’ Contributed to the 5th MATHMOD, Vienna.
  • Burger M, Osher S. . ‘A survey on level set methods for inverse problems and optimal design.’ European J. Appl. Math. 16: 263-301.
  • Burger M, Hofinger A. . ‘Greedy algorithms for neural network training with data noise.’ Computing 74: 1-22.
  • Wolfram M, Burger M. . ‘Inverse dopant profiling for highly doped semiconductor devices.’ Contributed to the 5th MATHMOD, Vienna.
  • Burger M, Gilboa G, Osher S, Xu J. . ‘Nonlinear inverse scale space methods for image restoration.’ Contributed to the Variational and Level Set Methods 2005.
  • Burger M. . ‘Numerical simulation of anisotropic surface diffusion with curvature-dependent energy.’ J. Comp. Phys. 203: 602-625.
  • Burger M, Hintermueller M. . ‘Projected gradient flows for BV / level set relaxation.’ PAMM 5, No. PAMM: 11-14.
  • Burger M, Gu H. . ‘Symbolic preprocessing of finite element methods for parameter-dependent geometric differential equations.’ Contributed to the Workshop on Symbolic-Numerical Computation 2005.
  • Osher S, Burger M, Goldfarb D, Xu J, Yin W. . ‘An iterative regularization method for total variation based image restoration.’ SIAM Multiscale Modelling and Simulation 4: 460-489.
  • Engwer C, Bastian P. . A Discontinuous Galerkin Method for Simulations in Complex Domains , .
  • Bastian P, Engwer C. . ‘Solving partial differential equations in complicated domains.’ Oberwolfach Reports 4.
  • Dreyer W, Herrmann M, Kunik M, Qamar S. . Kinetic schemes for selected initial and boundary value problems.’ In Analysis and numerics for conservation laws, edited by Warnecke G, 203-232. Springer Verlag. doi: 10.1007/3-540-27907-5_9.
  • Dedner A, Makridakis C, Ohlberger M. . ‘A new stable discontinuous Galerkin approximation for non-linear conservation laws on adaptively refined grids.’, 1095 - 1099.
  • Ohlberger M. . ‘A posterior error estimates for the heterogenoeous mulitscale finite element method for elliptic homogenization problems.’ SIAM Multiscale Mod. Simul. 4, No. 1: 88 - 114.
  • Ohlberger M. . ‘Error control for approximations of non-linear conservation laws.’, 85 - 100.
  • Bastian P, Droske M, Engwer C, Klöfkorn R, Neubauer T, Ohlberger M, Rumpf M. . ‘Towards a unified framework for scientific computing.’, 167 - 174.
  • Ohlberger M. . ‘A posteriori error estimates for the heterogeneous multiscale finite element method for elliptic homogenization problems.’ Multiscale Model. Simul. 4: 88-114.
  • Brancolini A., Buttazzo G. . Optimal networks for mass transportation problems.’ ESAIM: Control, Optimisation and Calculus of Variations null, No. 11: 88-101. doi: 10.1051/cocv:2004032.
  • Stevens A, Søgaard-Andersen L. . ‘Making waves: Pattern formation by a cell-surface-associated signal.’ Trends in Microbiology 13, No. 6: 249-252. doi: 10.1016/j.tim.2005.04.002.
  • Hwang HJ, Kang K, Stevens A. . Drift-diffusion limits of kinetic models for chemotaxis: A generalization.’ Discrete and Continuous Dynamical Systems - Series B 5, No. 2: 319-334.
  • Hwang H J, Kang K, Stevens A. . ‘Global solutions of nonlinear transport equations for chemosensitive movement.’ SIAM Journal on Mathematical Analysis 36, No. 4: 1177-1199. doi: 10.1137/S0036141003431888.
Submitted / Under Review
  • Surulescu C. . The Time Dependent Motion of a Navier-Stokes Fluid Through a Vessel With an Elastic Cover , .

  • Lunkenheimer PP, Redmann K, Florek J, Fassnacht U, Cryer CW, Wubbeling F, Niederer P. . ‘The forces generated within the musculature of the left ventricular wall.’ Heart 90, No. 2: 200-207. doi: 10.1136/hrt.2003.011650.
  • Burger M. . ‘Growth of multiple crystals in polymer melts.’ European J. Appl. Math. 15: 347-363.
  • Burger M, Hackl B, Ring W. . ‘Incorporating topological derivatives into level set methods.’ J. Comp. Phys. 194: 344-362.
  • Burger M, Osher S, Yablonovitch E. . ‘Inverse problem techniques for the design of photonic crystals.’ IEICE Transactions on Electronics 87 C: 258-265.
  • Ben Ameur H, Burger M, Hackl B. . ‘Level set methods for geometric inverse problems in linear elasticity.’ Inverse Problems 20: 673-696.
  • Burger M. . ‘Levenberg-Marquardt level set methods for inverse obstacle problems.’ Inverse Problems 20: 673-696.
  • Burger M, Engl H, Leitao A, Markowich P. . ‘On inverse problems for semiconductor equations.’ Milan J. Math. 72: 273-314.
  • Burger M, Capasso V, Micheletti A. . ‘Optimal control of polymer morphologies.’ J. Eng. Math. 49: 339-358.
  • Favaro P, Burger M, Soatto S. . ‘Scene and motion reconstruction from defocused and motion blurred images via anisotropic diffusion.’ Contributed to the ECCV.
  • Burger M, Osher S. . ‘Convergence rates of convex variational regularization.’ Inverse Problems 20: 1411-1421.
  • Bastian P, Droske M, Engwer C, Klöfkorn R, Neubauer T, Ohlberger M, Rumpf M. . ‘Towards a Unified Framework for Scientific Computing.’ In Proceedings of the 15th Conference on Domain Decomposition Methods. doi: 10.1007/3-540-26825-1_13.
  • Dreyer W, Herrmann M, Kunik M. . Kinetic solutions of the Boltzmann-Peierls equation and its moment systems.’ Continuum Mechanics and Thermodynamics 16, No. 5: 453-469. doi: 10.1007/s00161-003-0171-z.
  • Barth T, Ohlberger M. . ‘Finite volume methods: foundation and analysis.’, 439 -474.
  • Ohlberger M. . ‘Higher order finite volume methods on selfadaptive grids for convection dominated reactive transport problems in porous media.’ Comp. Vis. Sci. 7, No. 1: 41-51.
  • Horstmann Dirk, Stevens Angela. . ‘A constructive approach to traveling waves in chemotaxis.’ J. Nonlinear Sci. 14, no. 1: 1 - 25.

  • Lunkenheimer PP, Redmann K, Kimaun D, Cryer CW, Wubbeling F, Konertz W, Zytowsky A, Hotz H, Ho SY, Anderson RH. . ‘A critical evaluation of results of partial left ventriculectomy.’ Journal of Cardiac Surgery 18, No. 3: 225-235. doi: 10.1046/j.1540-8191.2003.02026.x.
  • Lunkenheimer PP, Redmann K, Cryer CW, Wubbeling F, Konertz W, Batista RJV, Ho SY, Anderson RH. . ‘The relationship between structure and function: why does reshaping the left ventricle surgically not always result in functional improvement?Computers in Biology and Medicine 33, No. 3: 185-196. doi: 10.1016/S0010-4825(02)00085-9.
  • Burger M, Pinnau R. . ‘Fast optimal design of semiconductor devices.’ SIAM J. Appl. Math. 64: 108-126.
  • Burger M. . ‘Growth and impingement in polymer melts.’ Contributed to the FBP 2002, Trento.
  • Burger M, Markowich P. . ‘Model reduction for semiconductor inverse dopant profiling.’ Contributed to the 4th IMACS Symposium on Mathematical Modelling, Wien, Österreich.
  • Burger M, Markowich P. . ‘Model reduction for semiconductor inverse dopant profiling.’ In Proceedings of the 4th IMACS Symposium on Mathematical Modelling, edited by Troch I, Breitenecker F.
  • Burger M. . ‘A framework for the construction of level set methods for shape optimization and reconstruction.’ Interfaces and Free Boundaries 5: 301-329.
  • Engwer C. . Direkte Simulation von Transportprozessen im Boden zur Bestimmung makroskopischer Parameter.
  • Kröner D, Küther M, Ohlberger M, Rohde C. . ‘A posteriori error estimates and adaptive methods for hyperbolic and convection dominates parabolic conservation laws.’, 289 - 306.
  • Küther M, Ohlberger M. . ‘Adaptive second order central schemes on unstructured staggered grids.’.
  • Haasdonk B, Ohlberger M, Rumpf M, Schmidt A, Siebert K. . ‘Multiresolution Visualization of Higher Order Adaptive Finite Element Simulations.’ Computing 70, No. Computing: 181--204.

  • Burger M, Neubauer A. . ‘Analysis of Tikhonov regularization for function approximation by neural networks.’ Neural Networks 16: 79-90.
  • Haslinger J, Bodenhofer U, Burger M. . ‘Data-Driven construction of Sugeno controllers: analytical aspects and new numerical methods.’ Contributed to the 9th IFSA World Congress and 20th NAFIPS International Conference, Vancouver.
  • Burger M, Engl H, Markowich P. . ‘Inverse doping problems for semiconductor devices.’ Contributed to the Recent Progress in Computational and Applied PDEs.
  • Burger M, Mühlhuber W. . ‘Iterative regularization of parameter identification problems by SQP methods.’ Inverse Problems 18: 943-970.
  • Burger M, Capasso V, Micheletti A. . ‘Mathematical modelling of the crystallization process of polymers.’ Contributed to the 5th Hellenic Conference on Computer Mathematics and its Applications, Athens.
  • Capasso V, Burger M, Micheletti A, Salani C. . ‘Mathematical models for polymer crystallization processes.’ In Mathematical modelling for polymer industry, edited by Capasso V, 167-242. Springer Verlag.
  • Burger M, Capasso V, Eder G. . ‘Modelling crystallization of polymers in temperature fields.’ ZAMM 82: 51-63.
  • Burger M, Capasso V, Salani C. . ‘Modelling multi-dimensional crystallization of polymers in interaction with heat transfer.’ Nonlinear Analysis: Real World Applications 3: 139-160.
  • Burger M, Haslinger J, Engl H, Bodenhofer U. . ‘Regularized data-driven construction of fuzzy controllers.’ J. Inverse Ill-Posed Problems 10: 319-344.
  • Haslinger J, Bodenhofer U, Burger M. . ‘Tuning of fuzzy systems as an ill-posed problem.’ Contributed to the ECMI 2000, Palermo.
  • Burger M, Mühlhuber W. . Numerical approximation of an SQP-type method for parameter identification.’ SIAM Journal on Numerical Analysis 40, No. 5: 1775--1797. doi: 10.1137/S0036142901389980.
  • Haslinger J, Bodenhofer U, Burger M. . ‘Tuning of fuzzy systems as an ill-posed problem.’ Contributed to the ECMI 2000, Palermo.
  • Dreyer W, Herrmann M, Kunik M. . Kinetic schemes and initial boundary value problems for the Euler system.’ Transport Theory and Statistical Physics 31, No. 1: 1-33. doi: 10.1081/TT-120003009.
  • Herbin R, Ohlberger M. . ‘A posteriori error estimate for finite volume approximations of convection diffusion problems.’.
  • Ohlberger M, Rohde C. . ‘Adaptive finite volume approximations for weakly coupled convection dominated parabolic systems.’ IMA J. Numer. Anal. 22, No. 2: 253 -280.
  • Bürkle D, Ohlberger M. . ‘Adaptive finite volume methods for displacement problems in porous media.’ Comp. Vis. Sci. 5, No. 2: 95 - 106.
  • Klöfkorn R, Kröner D, Ohlberger M. . ‘Local adaptive methods for convection dominated problems.’ International Journal for Numerical Methods in Fluids 40, No. 1-2: 79 - 91.
  • Karlsen KH, Ohlberger M. . ‘A note on the uniqueness of entropy solutions of nonlinear degenerate parabolic equations.’ J. Math. Anal. Appl. 275: 439-458.

  • Natterer F, Wübbeling F. . Mathematical methods in image reconstruction. Philadelphia, PA: Selbstverlag / Eigenverlag / Self-publishing. doi: 10.1118/1.1455744.
  • Burger M. . ‘A level set method for inverse problems.’ Inverse Problems 17: 1327-1356.
  • Burger M, Neubauer A. . ‘Error bounds for approximation with neural networks.’ J. Approx. Theory 112: 235-250.
  • Burger M, Engl H, Markowich P, Pietra P. . ‘Identification of doping profiles in semiconductor device.’ Inverse Problems 17: 1765-1795.
  • Burger M. . ‘Iterative regularization of a parameter identification problem occurring in polymer crystallization.’ SIAM J. Numer. Anal. 39, No. SIAM J. Numer. Anal.: 1029-1054.
  • Burger M, Capasso V. . ‘Mathematical modelling and simulation of non-isothermal crystallization of polymers.’ Math. Models and Methods in Appl. Sciences 11: 1029-1054.
  • Burger M, Scherzer O. . ‘Regularization methods for blind deconvolution and blind source separation problems.’ Mathematics of Control, Signals and Systems 14: 358-383.
  • Micheletti A, Burger M. . Stochastic and deterministic simulation of nonisothermal crystallization of polymers.’ Journal of Mathematical Chemistry 30, No. 2: 169--193. doi: 10.1023/A:1017923703579.
  • Ohlberger M. . ‘A posteriori error estimate for finite volume approximations to singularly perturbed nonlinear convection-diffusion equations.’ Numerische Mathematik 87, No. 4: 737 - 761.
  • Ohlberger M. . A posteriori error estimates and adaptive methods for convection dominated transport processes.
  • Haasdonk B, Ohlberger M, Rumpf M, Schmidt A, Siebert K. . h-p-Multiresolution Visualization of Adaptive Finite Element Simulations , .
  • Haasdonk B, Ohlberger M, Rozza G. . ‘A reduced basis method for evolution schemes with parameter-dependent explicit operators.’ Electron. Trans. Numer. Anal. 32: 145-161.
  • Ohlberger M. . ‘A posteriori error estimates for vertex centered finite volume approximations of convection-diffusion-reaction equations.’ M2AN Math. Model. Numer. Anal. 35: 355-387.
  • Heinze S, Papanicolaou G, Stevens A. . Variational principles for propagation speeds in inhomogeneous media.’ SIAM Journal on Applied Mathematics 62, No. 1: 129-148.

  • Burger M, Engl H. . ‘Training neural networks with noisy data as an ill-posed problem.’ Adv. Comp. Math 13, No. Adv. Comp. Math: 335-354.
  • Kröner D, Ohlberger M. . ‘A posteriori error estimates for upwind finite volume schemes for nonlinear conservation laws in multidimensions.’ Math. Comp. 69: 25-39.
  • Stevens A. . ‘The derivation of chemotaxis equations as limit dynamics of moderately interacting stochastic many-particle systems.’ SIAM Journal on Applied Mathematics 61, No. 1: 183-212. doi: 10.1137/S0036139998342065.
  • Stevens Angela. . ‘A stochastic cellular automaton modeling gliding and aggregation of myxobacteria.’ SIAM J. Appl. Math. 51, no. 1: 172 - 182.

  • Burger M, Capasso V, Engl H. . ‘Inverse problems related to crystallization of polymers.’ Inverse Problems 15, No. Inverse Problems: 155-173.
  • Burger M, Capasso V, Eder G, Engl H. . ‘Modelling and parameter-identification in non-isothermal crystallization of polymers.’ Contributed to the EcMI 98, Gothenburg.
  • Geßner T, Haasdonk B, Kende R, Lenz M, Metscher M, Neubauer R, Ohlberger M, Rosenbaum W, Rumpf M, Schwörer R, Spielberg M, Weikard U. . A Procedural Interface for Multiresolutional Visualization of General Numerical Data , .
  • Ohlberger M. . ‘Adaptive mesh refinement for single and two phase flow problems in porous media.’.
  • Ohlberger M, Rumpf M. . ‘Adaptive protection operators in multiresolution scientific visualizations.’ IEEE Transactions on Visualization and Computer Graphics 5, No. 1: 74 - 94.
  • Ohlberger M. . ‘Mixed finite element-finte volume methods for two-phase flow in porous media.’.
  • Grüne L, Metscher M, Ohlberger M. . ‘On numerical algorithm and interactive visualization for optimal control problems.’ Comp. Visual. Sci. 1, No. 4: 221 - 229.

  • Sonoc, C. . ‘On the Pathwise Uniqueness of Solutions of Stochastic Differential Equations.’ Portugaliae Mathematica 55: 451-456.
  • Ohlberger M, Schwörer R. . Challenges in Fluid Dynamics.

  • Sonoc, C. . ‘The Cauchy Problem for Seismic Wave Propagation.’ Analele Univ. de Vest din Timisoara, Seria Matematica/Informatica XXXV: 299-305.
  • Ohlberger M. . ‘Convergence of a mixed finite element-finite volume method for the two phase flow in porous media.’ East-West journal of numerical mathematics 5, No. 3: 183 - 210.
  • Neubauer R, Ohlberger M, Rumpf M, Schwörer R. . ‘Efficient visualization of large-scale data on hierarchical meshes.’.
  • Ohlberger M, Rumpf M. . ‘Hierarchical and adaptive visualization on nested grids.’ Computing 59, No. Computing: 365 - 385.
  • Othmer HG, Stevens A. . Aggregation, blowup, and collapse: The ABC'S of taxis in reinforced random walks.’ SIAM Journal on Applied Mathematics 57, No. 4: 1044-1081.
  • Stevens A, Schweitzer F. . ‘Aggregation induced by diffusing and non-diffusing media.’ In Dynamics of Cell and Tissue Motion, edited by Alt W, Deutsch A, Dunn G., 183-192. Birkhäuser Verlag.

  • Stevens A. . ‘Simulation of chemotaxis-equations in two space dimensions.’ In Nonlinear Physics of Complex Systems - Current Status and Future Trends, edited by Parisi J, Müller S C, Zimmermann W, 363-371.

  • Stevens Angela. . ‘Trail Following and Aggregation of Myxobacteria.’ Journal of Biological Systems 3, no. 4: 1059 - 1068.

  • Stevens A. . ‘Aggregation of Myxobacteria - a many particle system.’ Contributed to the First European Conference of Mathematics Applied to Biology and Medicine, l'Alpes d'Huez.

  • Stevens A. . ‘A model for gliding and aggregation of Myxobacteria.’ In Nonlinear wave processes in excitable media, edited by Holden A, Markus M, Othmer H G, 269-276.

  • Stevens A. . ‘Simulations of the aggregation and gliding behavior of Myxobacteria.’ In Biological motion. Lecture Notes in Biomathematics 89, edited by Alt W, Hoffmann G, 548-555. Springer Verlag.