Research

 

Research Areas

  • Numerical analysis for partial differential equations
  • Error control and adaptivity for finite element and finite volume schemes
  • Model reduction for parametrized partial differential equations
  • Development and analysis of numerical multiscale methods
  • Software development and scientific computing

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    Publications

    • Benner P, Grundel S, Himpe C.Parametric Model Order Reduction for Gas Flow Models.’ contributed to the MoRePaS 4 - Model Reduction for Parameterized Systems, Nantes, Frankreich, . doi: 10.14293/P2199-8442.1.SOP-MATH.EJOCET.v1.
    • Benner P, Grundel S, Himpe C, Huck C, Streubel T, Tischendorf C. . ‘Gas Network Benchmark Models.’ In Applications of Differential-Algebraic Equations: Examples and Benchmarks, edited by Campbell S, Ilchmann A, Mehrmann V, Reis T, 171-197. doi: 10.1007/11221_2018_5.
    • Benner P, Himpe C, Mitchell T. . ‘On Reduced Input-Output Dynamic Mode Decomposition.’ Advances in Computational Mathematics 44, No. 6: 1751-1768. doi: 10.1007/s10444-018-9592-x.
    • Dennis Eickhorn. . Randomisierte lokalisierte Modellreduktion mit Robin-Transferoperator (Masterarbeit).
    • Gallistl D, Henning P, Verfürth B. . ‘Numerical homogenization of H(curl)-problems.’ SIAM J. Numer. Anal. 56, No. 3: 1570-1596. doi: 10.1137/17M1133932.
    • Himpe C. . ‘emgr - The Empirical Gramian Framework.’ Algorithms 11, No. 7: 91. doi: 10.3390/a11070091.
    • Himpe C, Leibner T, Rave S. . Hierarchical Approximate Proper Orthogonal Decomposition.’ SIAM J. Sci. Comput. 40, No. 5: A3267-A3292.
    • Himpe C, Leibner T, Rave S.HAPOD - Fast, Simple and Reliable Distributed POD Computation.’ contributed to the MATHMOD 2018- 9th Vienna International Conference on Mathematical Modelling, Vienna, . doi: 10.11128/arep.55.a55283.
    • Ohlberger M, Verfürth B. . ‘A new Heterogeneous Multiscale Method for the Helmholtz equation with high contrast.’ Multiscale Model. Simul. 16, No. 1: 385-411. doi: 10.1137/16M1108820.
    • Ohlberger Mario, Rave Stephan, Schindler Felix, Wedemeier Tobias. . ‘Model reduction for parameterized systems and inverse problems.’ Oberwolfach Reports 2018, No. 39: 2454-2457. doi: 10.4171/OWR/2018/39.
    • Ohlberger Mario, Schaefer Michael, Schindler Felix. . Localized Model Reduction in PDE Constrained Optimization.’ In Shape Optimization, Homogenization and Optimal Control – DFG-AIMS workshop held at the AIMS Center Senegal, March 13-16, 2017, edited by Schulz V, Seck D, 143-163. Basel: Birkhäuser. doi: 10.1007/978-3-319-90469-6_8.
    • Verfürth B. . Heterogeneous Multiscale Method for the Maxwell equations with high contrast.’ ESAIM Math. Model. Numer. Anal. xx. [Accepted]
    • Verfürth B. . Numerical multiscale methods for Maxwell's equations in heterogeneous media Doctoral Thesis, Universität Münster.

    • Bastian P, Engwer C, Fahlke J, Geveler M, Göddeke D, Iliev O, Ippisch O, Milk R, J M, Müthing S, Ohlberger M, Ribbrock D, Turek S. . ‘Advances concerning multiscale methods and uncertainty quantification in EXA-DUNE.’ In Software for Exascale Computing - SPPEXA 2013-2015, edited by Hans-Joachim Bungartz, Philipp Neumann, Wolfgang E. Nagel, 25-43. doi: 10.1007/978-3-319-40528-5_2.
    • Bastian P, Engwer C, Fahlke J, Geveler M, Göddeke D, Iliev O, Ippisch O, Milk R, J M, Müthing S, Ohlberger M, Ribbrock D, Turek S. . ‘Hardware-based Efficiency Advances in the EXA-DUNE Project.’ In Software for Exascale Computing - SPPEXA 2013-2015, edited by Hans-Joachim Bungartz, Philipp Neumann, Wolfgang E. Nagel, 3-23. Springer. doi: 10.1007/978-3-319-40528-5_1.
    • Brunken Julia, Leibner Tobias, Ohlberger Mario, Smetana Kathrin. . Problem adapted hierachical model reduction for the Fokker-Planck equation.’ In ALGORITMY 2016 Proceedings of contributed papers and posters, edited by Handlovicova Angela, Sevcovic Daniel, 13-22. Bratislava: Slovak University of Technology in Bratislava.
    • Engwer C, Henning P, M\ralqvist A, Peterseim D. . Efficient implementation of the Localized Orthogonal Decomposition method arXiv, . [Submitted]
    • Falconi Delgado C, Lehrenfeld C, Marschall H, Meyer C, Abiev R, Bothe D, Reusken A, Schlüter M, Wörner M. . ‘Numerical and Experimental Analysis of Local Flow Phenomena in Laminar Taylor Flow in a Square Mini-Channel.’ Physics of Fluids 28, No. 1: 012109.
    • Fehr J, Heiland J, Himpe C, Saak J. . ‘Best Practices for Replicability, Reproducibility and Reusability of Computer-Based Experiments Exemplified by Model Reduction.’ AIMS Mathematics 1, No. 3: 261--281. doi: 10.3934/Math.2016.3.261.
    • Henning P, Ohlberger M. . ‘A-posteriori error estimate for a heterogeneous multiscale approximation of advection-diffusion problems with large expected drift.’ Discrete and Continuous Dynamical Systems - Series S 9, No. 5: 1393-1420. doi: 10.3934/dcdss.2016056.
    • Henning P, Ohlberger M, Verfürth B. . ‘A new Heterogeneous Multiscale Method for time-harmonic Maxwell's equations.’ SIAM J. Numer. Anal. 54, No. 6: 3493-3522. doi: 10.1137/15M1039225.
    • Henning P, Ohlberger M, Verfürth B. . ‘Analysis of multiscale methods for time-harmonic Maxwell's equations.’ Proc. Appl. Math. Mech. 16, No. 1: 559-560. doi: 10.1002/pamm.201610268.
    • Himpe C, Ohlberger M. . ‘A note on the cross Gramian for non-symmetric systems.’ System Science and Control Engineering 4, No. 1: 199-208. doi: 10.1080/21642583.2016.1215273.
    • Lehrenfeld C, Reusken A. . ‘Analysis of a high order unfitted finite element method for elliptic interface problems.’ arXiv preprint arXiv:1602.02970 1602.02970. [Submitted]
    • Lehrenfeld C, Reusken A. . ‘Optimal Preconditioners for Nitsche-XFEM Discretizations of Interface Problems.’ Numerische Mathematik 2016. doi: 10.1007/s00211-016-0801-6.
    • Lehrenfeld C, Reusken A. . L2-estimates for a high order unfitted finite element method for elliptic interface problems : arXiv eprints, . [Submitted]
    • Lehrenfeld C, Schöberl J. . ‘High order exactly divergence-free Hybrid Discontinuous Galerkin Methods for unsteady incompressible flows.’ Comp. Meth. Appl. Mech. Eng. 2016. doi: 10.1016/j.cma.2016.04.025. [In Press]
    • Lehrenfeld Christoph. . High order unfitted finite element methods on level set domains using isoparametric mappings.’ Comp. Meth. Appl. Mech. Eng. 300, No. 1: 716-733. doi: 10.1016/j.cma.2015.12.005.
    • Milk R, Rave S, Schindler F. . pyMOR - Generic algorithms and interfaces for model order reduction.’ SIAM Journal on Scientific Computing 38, No. 5: 194-216. doi: 10.1137/15M1026614.
    • Ohlberger M, Rave S. . Reduced Basis Methods: Success, Limitations and Future Challenges.’ In roceedings of ALGORITMY 2016, 20th Conference on Scientific Computing, Vysoke Tatry, Podbanske, Slovakia, March 13-18, 2016, edited by A. Handlovičova and D. Sevčovič, 1-12. Bratislava: Publishing House of Slovak University of Technology in Bratislava.
    • Ohlberger M, Rave S, Schindler F. . ‘Adaptive Localized Model Reduction.’ Oberwolfach Reports 13, No. 3: 2406-2409. doi: 10.4171/OWR/2016/42.
    • Ohlberger M, Rave S, Schindler F. . Model Reduction for Multiscale Lithium-Ion Battery Simulation.’ In Numerical Mathematics and Advanced Applications ENUMATH 2015, edited by Karasözen B, Manguoğlu M, Teuer-Sezgin M, Göktepe S, Uğur Ö, 317-331.: Springer. doi: 10.1007/978-3-319-39929-4_31.
    • Ohlberger M, Smetana K. . Approximation of skewed interfaces with tensor-based model reduction procedures: application to the reduced basis hierarchical model reduction approach.’ J. Comp. Phys. 321: 1185-1205. doi: 10.1016/j.jcp.2016.06.021.
    • Schindler, F. . Model reduction for parametric multi-scale problems Doctoral Thesis, Westfälische Wilhelms-Universität Münster.
    • Smetana Kathrin, Patera Anthony T. . ‘Optimal local approximation spaces for component-based static condensation procedures.’ SIAM J. Sci. Comput. 38, No. 5: A3318--A3356. doi: 10.1137/15M1009603.

    • Benner P, Ohlberger M, Patera A, Rozza G, Sorensen D, Urban K. . ‘Model order reduction of parameterized systems (MoRePaS).’ Adv. Comp. Math 41, No. 5: 955-960. doi: 10.1007/s10444-015-9443-y.
    • Buhr A, Ohlberger M. . ‘Interactive Simulations Using Localized Reduced Basis Methods.’ In IFAC-PapersOnLine, 729-730. doi: 10.1016/j.ifacol.2015.05.134.
    • Henning P, Ohlberger M. . ‘Error control and adaptivity for heterogeneous multiscale approximations of nonlinear monotone problems.’ Discrete and Continuous Dynamical Systems - Series S 8, No. 1: 119-150. doi: 10.3934/dcdss.2015.8.119.
    • Henning P, Ohlberger M, Schweizer B. . ‘Adaptive Heterogeneous Multiscale Methods for immiscible two-phase flow in porous media.’ Computational Geosciences 1, No. 19: 99--114. doi: 10.1007/s10596-014-9455-6.
    • Himpe C, Ohlberger M. . ‘Data-driven combined state and parameter reduction for inverse problems.’ Advances in Computational Mathematics 41, No. 5: 1343-1364. doi: 10.1007/s10444-015-9420-5.
    • Himpe C, Ohlberger M.Accelerating the Computation of Empirical Gramians and Related Methods.’ contributed to the 5th International Workshop on Model Reduction in Reacting Flows, Spreewald, . doi: 10.5281/zenodo.46643.
    • Himpe C, Ohlberger M. . ‘The Empirical Cross Gramian for Parametrized Nonlinear Systems.’ Contributed to the MATHMOD 2015 - 8th Vienna International Conference on Mathematical Modelling, Vienna. doi: 10.1016/j.ifacol.2015.05.163.
    • Himpe C, Ohlberger M.The Versatile Cross Gramian.’ contributed to the Model Reduction for Parameterized Systems (MoRePaS) III, Trieste, Italy, . doi: 10.14293/P2199-8442.1.SOP-MATH.PSAHPZ.v1.
    • Kaulmann S, Flemisch B, Haasdonk B, Lie K, Ohlberger M. . ‘The Localized Reduced Basis Multiscale method for two-phase flows in porous media.’ International Journal for Numerical Methods in Engineering 5, No. 102: 1018-1040. doi: 10.1002/nme.4773.
    • Lehrenfeld C. . ‘The Nitsche XFEM-DG Space-Time Method and its Implementation in Three Space Dimensions.’ SIAM J. Sci. Comput. 37: A245-A270. doi: 10.1137/130943534.
    • Lehrenfeld C. . On a Space-Time Extended Finite Element Method for the Solution of a Class of Two-Phase Mass Transport Problems Doctoral Thesis, RWTH Aachen.
    • Lehrenfeld C, Reusken A. . ‘Finite Element Techniques for the Numerical Simulation of Two-Phase Flows with Mass Transport.’ In Computational Methods for Complex Liquid-Fluid Interfaces, edited by CRC Press, 353-371.
    • Leibner Tobias. . Numerical methods for kinetic equations (Master's thesis).
    • Mohring Jan, Milk Rene, Ngo Adrian, Klein Ole, Iliev Oleg, Ohlberger Mario, Bastian Peter. . ‘Uncertainty Quantification for Porous Media Flow Using Multilevel Monte Carlo.’ In Proceedings of 10th International Conference on Large-Scale Scientific Computations, Sozopol 2015, edited by Lirkov I., Margenov S. D. , Wasniewski J., 145-152.: Springer International Publishing. doi: 10.1007/978-3-319-26520-9_15.
    • Ohlberger M, Schindler F. . Error control for the localized reduced basis multi-scale method with adaptive on-line enrichment.’ SIAM J. Sci. Comput. 37, No. 6: A2865-A2895. doi: 10.1137/151003660.
    • Ohlberger Mario, Smetana Kathrin. . ‘A Dimensional Reduction Approach Based on the Application of Reduced Basis Methods in the Framework of Hierarchical Model Reduction.’ Oberwolfach Reports 2/2015: 141-144. doi: 10.4171/OWR/2015/2.
    • Smetana Kathrin. . A new certification framework for the port reduced static condensation reduced basis element method.’ Computer Methods in Applied Mechanics and Engineering 283: 352-383. doi: 10.1016/j.cma.2014.09.020.

    • Bastian P, Engwer C, Göddeke D, Iliev O, Ippisch O, Ohlberger M, Turek S, Fahlke J, Kaulmann S, Müthing S, Ribbrock D. . ‘EXA-DUNE: Flexible PDE Solvers, Numerical Methods and Applications.’ In Euro-Par 2014: Parallel Processing Workshops, edited by Lopes L., Žilinskas J., Costan A., Cascella R.G., Kecskemeti G., Jeannot E., Cannataro M., Ricci L., Benkner S., Petit S., Scarano V., Gracia J., Hunold S., Scott S.L., Lankes S., Lengaue C., Carretero J., Breitbart J., Alexander M., 530-541. Springer International Publishing. doi: 10.1007/978-3-319-14313-2_45.
    • Berninger H, Ohlberger M, Sander O, Smetana K. . Unsaturated subsurface flow with surface water and nonlinear in- and outflow conditions.’ Math. Models and Methods in Appl. Sciences 24, No. 5: 901-936. doi: 10.1142/S0218202513500711.
    • Buhr A, Engwer C, Ohlberger M, Rave S. . A Numerically Stable A Posteriori Error Estimator for Reduced Basis Approximations of Elliptic Equations.’ In 11th World Congress on Computational Mechanics, WCCM 2014, 5th European Conference on Computational Mechanics, ECCM 2014 and 6th European Conference on Computational Fluid Dynamics, ECFD 2014, edited by E. Onate XO, Huerta A, 4094-4102.: CIMNE, Barcelona.
    • Fuhrmann J, Ohlberger M, Rohde C. . Finite Volumes for Complex Applications VII-Elliptic, Parabolic and Hyperbolic Problems - FVCA 7, Berlin, June 2014.: Springer International Publishing. doi: 10.1007/978-3-319-05591-6.
    • Fuhrmann J, Ohlberger M, Rohde C. . Finite Volumes for Complex Applications VII-Methods and Theoretical Aspects - FVCA 7, Berlin, June 2014.: Springer International Publishing. doi: 10.1007/978-3-319-05684-5.
    • Girke S, Klöfkorn R, Ohlberger M. . Efficient Parallel Simulation of Atherosclerotic Plaque Formation Using Higher Order Discontinuous Galerkin Schemes.’ In Finite Volumes for Complex Applications VII-Elliptic, Parabolic and Hyperbolic Problems, edited by Fuhrmann J, Ohlberger M, Rohde C, 617-625.: Springer International Publishing. doi: 10.1007/978-3-319-05591-6_61.
    • Haasdonk B, Ohlberger M. . Wenn die Probleme zahlreicher werden: Reduzierte Basis Methoden f\ür effiziente und gesicherte numerische Simulation.“ GAMM Rundbrief 2014/1: 6-13.
    • Henning Patrick, Ohlberger Mario, Schweizer Benn. . ‘An adaptive Multiscale Finite Element Method.’ Multiscale Mod. Simul. 12, No. 3: 1078-1107. doi: 10.1137/120886856.
    • Himpe C, Ohlberger M. . ‘Cross-Gramian Based Combined State and Parameter Reduction for Large-Scale Control Systems.’ Mathematical Problems in Engineering 2014: 1-13. doi: 10.1155/2014/843869.
    • Himpe C, Ohlberger M. . ‘Model Reduction for Complex Hyperbolic Networks.’ Contributed to the 13th European Control Conference (ECC), June 24-27, 2014, Strasbourg, France. doi: 10.1109/ECC.2014.6862188.
    • Himpe C, Ohlberger M. . ‘Combined State and Parameter Reduction.’ Contributed to the 85th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM), Erlangen. doi: 10.1002/pamm.201410393.
    • Marschall H, Boden S, Lehrenfeld C, Falconi Delgado C, Hampel U, Reusken A, Wörner M, Bothe D. . ‘Validation of Interface Capturing and Tracking Techniques with different Surface Tension Treatments against a Taylor Bubble Benchmark Problem.’ Comput. & Fluids 102: 336-352. doi: 10.1016/j.compfluid.2014.06.030.
    • Mikula K, Ohlberger M, Urban J. . ‘Inflow-Implicit/Outflow-Explicit Finite Volume Methods for Solving Advection Equations.’ Applied Numerical Mathematics 85: 16-37. doi: 10.1016/j.apnum.2014.06.002.
    • Ohlberger M, Rave S, Schmidt S, Zhang S. . ‘A Model Reduction Framework for Efficient Simulation of Li-Ion Batteries.’ In Finite Volumes for Complex Applications VII-Elliptic, Parabolic and Hyperbolic Problems, edited by Fuhrmann J, Ohlberger M, Rohde C, 695-702.: Springer. doi: 10.1007/978-3-319-05591-6_69.
    • Ohlberger M, Schindler F. . A-Posteriori Error Estimates for the Localized Reduced Basis Multi-Scale Method.’ In Finite Volumes for Complex Applications VII-Methods and Theoretical Aspects, edited by , Rohde C, 421-429.: Springer International Publishing. doi: 10.1007/978-3-319-05684-5_41.
    • Ohlberger M, Smetana K. . ‘A Dimensional Reduction Approach Based on the Application of Reduced Basis Methods in the Framework of Hierarchical Model Reduction.’ SIAM J. Sci. Comput. 36, No. 2: A714-A736. doi: 10.1137/130939122.

    • Aland S, Lehrenfeld C, Marschall H, Meyer C, Weller S. . ‘Accuracy of Two-Phase Flow Simulations.’ In Proc. Appl. Math. Mech., 595-598.: Springer. doi: 10.1002/pamm.201310278.
    • Albrecht F, Ohlberger M. . The localized reduced basis multi-scale method with online enrichment.’ Oberwolfach Reports 7: 406-409. doi: 10.4171/OWR/2013/07.
    • Henning P, Ohlberger M, Schweizer B. . Homogenization of the degenerate two-phase flow equations.’ Math. Models and Methods in Appl. Sciences 23, No. 12: 2323-2352. doi: 10.1142/S0218202513500334.
    • Himpe C, Ohlberger M. . ‘A Unified Software Framework for Empirical Gramians.’ Journal of Mathematics 2013, No. 2013: 1-6. doi: 10.1155/2013/365909.
    • Lehrenfeld C, Reusken A. . ‘Analysis of a DG-XFEM Discretization for a Class of Two-Phase Mass Transport Problems.’ SIAM J. Numer. Anal. 51: 958-983. doi: 10.1137/120875260.
    • Ohlberger M, Albrecht F, Drohmann M, Henning P, Kaulmann S, Schweizer B. . Model reduction for multiscale problems.’ Oberwolfach Reports 39: 2228-2230. doi: 10.4171/OWR/2013/39.
    • Ohlberger M, Rave S. . ‘Nonlinear reduced basis approximation of parameterized evolution equations via the method of freezing.’ C. R. Acad. Sci. Paris, Ser. I 351: 901-906. doi: 10.1016/j.crma.2013.10.028.
    • Ohlberger M, Schaefer M. . ‘Error Control Based Model Reduction for Parameter Optimization of Elliptic Homogenization Problems.’ In Proceedings of the 1st IFAC Workshop on Control of Systems Governed by Partial Differential Equations. doi: 10.3182/20130925-3-FR-4043.00053.
    • Schöberl J, Lehrenfeld C. . ‘Domain Decomposition Preconditioning for High Order Hybrid Discontinuous Galerkin Methods on Tetrahedral Meshes.’ In Advanced Finite Element Methods and Applications, edited by Apel Thomas, Steinbach Olaf, 27-56. Springer.

    • Albrecht F, Haasdonk B, Kaulmann S, Ohlberger M. . The Localized Reduced Basis Multiscale Method.’ Contributed to the Algoritmy 2012, Conference on Scientific Computing, Vysoke Tatry, Podbanske, September 9-14, 2012, Vysoke Tatry, Podbanske.
    • Bastian P, Berninger H, Dedner A, Engwer C, Henning P, Kornhuber R, Kröner D, Ohlberger M, Sander O, Schiffler G, Shokina N, Smetana K. . Adaptive Modelling of Coupled Hydrological Processes with Application in Water Management.’ In Progress in Industrial Mathematics at ECMI 2010, 561--567.: Springer,. doi: 10.1007/978-3-642-25100-9_65.
    • Bernard-Champmartin A, Deriaz E, Hoch P, Samba G, Schaefer M. . ‘Extension of centered hydrodynamical schemes to unstructured deforming conical meshes: the case of circles.’ In CEMRACS'11: Multiscale Coupling of Complex Models in Scientific Computing, 135-162.: ESAIM: Proceedings. doi: 10.1051/proc/201238008.
    • Drohmann Martin , Haasdonk Bernard, Ohlberger, Mario. . ‘Reduced Basis Model Reduction of Parametrized Two-Phase Flow in Porous Media.’ In 7th Vienna International Conference on Mathematical Modelling, 722-727. doi: 10.3182/20120215-3-AT-3016.00128.
    • Koutschan Christoph, Lehrenfeld Christoph, Schöberl Joachim. . ‘Computer Algebra meets Finite Elements: an Efficient Implementation for Maxwells Equations.’ In Numerical and Symbolic Scientific Computing: Progress and Prospects, edited by Ulrich Langer PP, 105-122. Springer. doi: 10.1007/978-3-7091-0794-2_6.
    • Lehrenfeld Christoph, Reusken Arnold. . ‘Nitsche-XFEM with Streamline Diffusion Stabilization for a Two-Phase Mass Transport Problem.’ SIAM J. Sci. Comput. 34: 2740-2759. doi: 10.1137/110855235.
    • Ohlberger M. . Error control based model reduction for multiscale problems.’ In Proceedings of Algoritmy 2012, Conference on Scientific Computing, Vysoke Tatry, Podbanske, September 9-14, 2012, edited by Slovak University of Technology in Bratislava, Publishing House of STU, 1-10.
    • Ohlberger M, Schaefer M. . A reduced basis method for parameter optimization of multiscale problems.’ In Submitted to Algoritmy 2012, Conference on Scientific Computing, Vysoke Tatry, Podbanske, September 9-14, 2012.
    • Rave S. . On Finitely Summable K-Homology Doctoral Thesis, Universität Münster.

    • Drohmann M, Haasdonk B, Ohlberger M. . ‘Adaptive Reduced Basis Methods for Nonlinear Convection-Diffusion Equations.’ In Finite Volumes for Complex Applications VI - Problems & Perspectives, edited by Fort J. et al., 369--377.: Springer. doi: 10.1007/978-3-642-20671-9_39.
    • Haasdonk B, Dihlmann M, Ohlberger M. . ‘A Training Set and Multiple Bases Generation Approach for Parametrized Model Reduction Based on Adaptive Grids in Parameter Space.’ Mathematical and Computer Modelling of Dynamical Systems 2011, No. 17 (4): 423--442. doi: 10.1080/13873954.2011.547674.
    • Haasdonk B, Ohlberger M. . ‘Efficient reduced models and a posteriori error estimation for parametrized dynamical systems by offline/online decomposition.’ Mathematical and Computer Modelling of Dynamical Systems 17, No. 2: 145--161. doi: 10.1080/13873954.2010.514703.
    • Henning P, Ohlberger M. . ‘A Note on Homogenization of Advection-Diffusion Problems with Large Expected Drift.’ Zeitschrift für Analysis und ihre Anwendungen 2011, No. 30(3): 319--339. doi: 10.4171/ZAA/1437.
    • Lehrenfeld Christoph. . ‘Nitsche-XFEM for a Transport Problem in Two- Phase Incompressible Flows.’ In Proc. Appl. Math. Mech., 613-614.: Wiley. doi: 10.1002/pamm.201110296.
    • Mikula K, Ohlberger M. . ‘Inflow-Implicit/Outflow-Explicit scheme for solving advection equations.’ In Finite Volumes for Complex Applications VI - Problems & Perspectives, edited by Fort J. et al., 683--691.: Springer. doi: 10.1007/978-3-642-20671-9_72.
    • Ohlberger M, Smetana K. . ‘A new Hierarchical Model Reduction-Reduced Basis technique for advection-diffusion-reaction problems.’ In Proceedings of the V International Conference on Adaptive Modeling and Simulation (ADMOS 2011) held in Paris, France, 6-8 June 2011, edited by Aubry D. et al., 343-354.: International Center for Numerical Methods in Engineering (CIMNE), Barcelona.

    • Dedner A, Klöfkorn R, Nolte M, Ohlberger M. . ‘A generic interface for parallel and adaptive scientific computing: Abstraction principles and the DUNE-FEM module.’ Computing 90, No. 3-4: 165-196. doi: 10.1007/s00607-010-0110-3.
    • Drohmann M, Haasdonk B, Ohlberger M. . Reduced Basis Approximation for Nonlinear Parametrized Evolution Equations based on Empirical Operator Interpolation , .
    • Henning P, Ohlberger M. . ‘The heterogeneous multiscale finite element method for advection-diffusion problems with rapidly oscillating coefficients and large expected drift.’ Networks and Heterogeneous Media 5, No. 4: 711--744. doi: 10.3934/nhm.2010.5.711.
    • Lehrenfeld Christoph. . Hybrid Discontinuous Galerkin Methods for Incompressible Flow Problems.
    • Mikula K, Ohlberger M. . A New Inflow-Implicit/Outflow-Explicit Finite Volume Method for Solving Variable Velocity Advection Equations , .
    • Mikula K, Ohlberger M. . ‘A New Level Set Method for Motion in Normal Direction Based on a Semi-Implicit Forward-Backward Diffusion Approach.’ SIAM J. Sci. Comput. 32, No. 3: 1527--1544. doi: 10.1137/09075946X.
    • Ohlberger M, Smetana K. . A new problem adapted hierarchical model reduction technique based on reduced basis methods and dimensional splitting , .

    • Albrecht F. . Local Discontinuous Galerkin Verfahren für die Stokes Gleichungen und Homogenisierung in porösen Medien (Diplomarbeit).
    • Drohmann M, Haasdonk B, Ohlberger M. . ‘Reduced Basis Method for Finite Volume Approximation of Evolution Equations on Parametrized Geometries.’ Contributed to the Proceedings of ALGORITMY 2009.
    • Haasdonk B, Ohlberger M. . ‘Efficient reduced models for parametrized dynamical systems by offline/online decomposition.’.
    • Haasdonk B, Ohlberger M. . ‘Space-adaptive reduced basis simulation for time-dependent problems.’.
    • Haasdonk B, Ohlberger M. . ‘Reduced Basis Method for Explicit Finite Volume Approximations of Nonlinear Conservation Laws.’ In Hyperbolic problems: theory, numerics and applications. Providence, RI: Amer. Math. Soc.
    • Henning P, Ohlberger M. . ‘The heterogeneous multiscale finite element method for elliptic homogenization problems in perforated domains.’ Numer. Math. 113: 601-629. doi: 10.1007/s00211-009-0244-4.
    • Henning P, Ohlberger M. . A-posteriori error estimate for a heterogeneous multiscale finite element method for advection-diffusion problems with rapidly oscillating coefficients and large expected drift. , .
    • Ohlberger M. . ‘A review of a posteriori error control and adaptivity for approximations of nonlinear conservation laws.International Journal for Numerical Methods in Fluids 59, No. International Journal for Numerical Methods in Fluids: 333--354. doi: 10.1002/fld.1686.

    • 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.
    • 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.
    • 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.
    • 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.
    • 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. doi: 10.1007/978-3-540-69010-8_7.
    • 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.

    • 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.
    • 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 , No. Journal of Fuel Cell Science and Technology.
    • Haasdonk B, Ohlberger M. . ‘Basis Construction for Reduced Basis Methods by Adaptive Parameter Grids.’.
    • Henning P. . Die Heterogene Mehrskalenmethode f\�r elliptische Differentialgleichungen in perforierten Gebieten.
    • Klöfkorn R, Kröner D, Ohlberger M. . ‘Parallel and adaptive simulaiton of fuel cells in 3D.’.
    • 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.
    • Rave S. . Über die Entscheidbarkeit gewisser Prädikate in der Theorie der C*-Algebren. Münster.

    • 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.

    • Bastian P, Droske M, Engwer C, Klöfkorn R, Neubauer T, Ohlberger M, Rumpf M. . ‘Towards a unified framework for scientific computing.’, 167 - 174.
    • 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 posteriori error estimates for the heterogeneous multiscale finite element method for elliptic homogenization problems.’ Multiscale Model. Simul. 4: 88-114.
    • 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.

    • 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.

    • 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.
    • 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.’.

    • Bürkle D, Ohlberger M. . ‘Adaptive finite volume methods for displacement problems in porous media.’ Comp. Vis. Sci. 5, No. 2: 95 - 106.
    • Herbin R, Ohlberger M. . ‘A posteriori error estimate for finite volume approximations of convection diffusion problems.’.
    • Karlsen KH, Ohlberger M. . ‘A note on the uniqueness of entropy solutions of nonlinear degenerate parabolic equations.’ J. Math. Anal. Appl. 275: 439-458.
    • 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.
    • Ohlberger M, Rohde C. . ‘Adaptive finite volume approximations for weakly coupled convection dominated parabolic systems.’ IMA J. Numer. Anal. 22, No. 2: 253 -280.

    • 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.
    • Haasdonk B, Ohlberger M, Rumpf M, Schmidt A, Siebert K. . h-p-Multiresolution Visualization of Adaptive Finite Element Simulations , .
    • 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.
    • 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.

    • Kröner D, Ohlberger M. . ‘A posteriori error estimates for upwind finite volume schemes for nonlinear conservation laws in multidimensions.’ Math. Comp. 69: 25-39.

    • 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 , .
    • Grüne L, Metscher M, Ohlberger M. . ‘On numerical algorithm and interactive visualization for optimal control problems.’ Comp. Visual. Sci. 1, No. 4: 221 - 229.
    • Ohlberger M. . ‘Adaptive mesh refinement for single and two phase flow problems in porous media.’.
    • Ohlberger M. . ‘Mixed finite element-finte volume methods for two-phase flow 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, Schwörer R. . Challenges in Fluid Dynamics.

    • Neubauer R, Ohlberger M, Rumpf M, Schwörer R. . ‘Efficient visualization of large-scale data on hierarchical meshes.’.
    • 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.
    • Ohlberger M, Rumpf M. . ‘Hierarchical and adaptive visualization on nested grids.’ Computing 59, No. Computing: 365 - 385.

  •  

    Habilitations

    Henning, PatrickApplications of numerical homogenization in geosciences and physics
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    Dissertations

    Leibner, TobiasModel reduction for kinetic equations: moment approximations and hierarchical approximate proper orthogonal decomposition
    Brunken, JuliaStable and efficient Petrov-Galerkin methods for certain (kinetic) transport equations
    Buhr, AndreasTowards Automatic and Reliable Localized Model Order Reduction. Local Training, a Posteriori Error Estimation and Online Enrichment.
    Verfürth, BarbaraNumerical multiscale methods for Maxwell's equations in heterogeneous media
    Himpe, ChristianCombined State and Parameter Reduction for Nonlinear Systems with an Application in Neuroscience
    Schindler, FelixModel Reduction for Parametric Multi-Scale Problems
    Kaulmann, SvenEfficient Schemes for Parameterized Multiscale Problems
    Smetana, KathrinA dimensional reduction approach based on the application of reduced basis methods in the context of hierarchical model reduction
    Drohmann, MartinReduced basis model reduction for non-linear evolution equations
    Henning, PatrickHeterogeneous multiscale finite element methods for advection-diffusion and nonlinear elliptic multiscale problems
    Klöfkorn RobertNumerics for Evolution Equations - A General Interface Based Design Concept