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

    • Leibner Tobias. . Numerical methods for kinetic equations (Master's thesis).
    • 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.
    • 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.
    • 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.
    • Himpe Christian, Ohlberger Mario.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.
    • 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 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.
    • Himpe C, Ohlberger M. . Accelerating the Computation of Empirical Gramians and Related Methods.
    • Himpe C, Ohlberger M. . ‘The Empirical Cross Gramian for Parametrized Nonlinear Systems.’ In MATHMOD 2015 - 8th Vienna International Conference on Mathematical Modelling, 727-728.: IFAC. doi: 10.1016/j.ifacol.2015.05.163.
    • 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.
    • 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.
    • 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: http://dx.doi.org/10.1016/j.cma.2014.09.020.
    • 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.
    • Buhr A, Ohlberger M. . ‘Interactive Simulations Using Localized Reduced Basis Methods.’ In IFAC-PapersOnLine, 729-730. doi: 10.1016/j.ifacol.2015.05.134.
    • 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.
    • 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.

    • Himpe C, Ohlberger M. . ‘A Unified Software Framework for Empirical Gramians.’ Journal of Mathematics 2013, No. 2013: 1-6. doi: 10.1155/2013/365909.
    • 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.
    • 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.
    • 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.
    • 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.
    • 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.
    • 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.
    • 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.

    • 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.
    • Rave S. . On Finitely Summable K-Homology Doctoral Thesis, Universität Münster.
    • 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.
    • 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.
    • 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.
    • 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.
    • Albrecht F, Haasdonk B, Ohlberger M, Kaulmann S. . 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.

    • 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.
    • 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.
    • 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.
    • 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.
    • 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.
    • 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.

    • Lehrenfeld Christoph. . Hybrid Discontinuous Galerkin Methods for Incompressible Flow Problems.
    • 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.
    • 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.
    • 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 , .
    • Ohlberger M, Smetana K. . A new problem adapted hierarchical model reduction technique based on reduced basis methods and dimensional splitting , .
    • Mikula K, Ohlberger M. . A New Inflow-Implicit/Outflow-Explicit Finite Volume Method for Solving Variable Velocity Advection Equations , .
    • Schaefer, Michael. . Parameteroptimierung für elliptische Differentialgleichungen mit Hilfe der Reduzierten Basis Methode.

    • 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.
    • 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. . ‘Space-adaptive reduced basis simulation for time-dependent problems.’.
    • Haasdonk B, Ohlberger M. . ‘Efficient reduced models for parametrized dynamical systems by offline/online decomposition.’.
    • 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. , .
    • 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.
    • 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.
    • Albrecht F. . Local Discontinuous Galerkin Verfahren für die Stokes Gleichungen und Homogenisierung in porösen Medien (Diplomarbeit).

    • 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.
    • 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.
    • 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.
    • 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.
    • 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.
    • 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.

    • 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.
    • Klöfkorn R, Kröner D, Ohlberger M. . ‘Parallel and adaptive simulaiton of fuel cells in 3D.’.
    • 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.’.
    • 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.

    • Haasdonk B, Ohlberger M. . Reduced Basis Method for Finite Volume Approximations of Parametrized Evolution Equations , .
    • 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.
    • 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.
    • Ohlberger M. . ‘Error control for approximations of non-linear conservation laws.’, 85 - 100.
    • 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. . ‘A posteriori error estimates for the heterogeneous multiscale finite element method for elliptic homogenization problems.’ Multiscale Model. Simul. 4: 88-114.

    • 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.
    • Barth T, Ohlberger M. . ‘Finite volume methods: foundation and analysis.’, 439 -474.

    • 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.
    • 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.

    • 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.
    • 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.’.
    • Ohlberger M, Rohde C. . ‘Adaptive finite volume approximations for weakly coupled convection dominated parabolic systems.’ IMA J. Numer. Anal. 22, No. 2: 253 -280.
    • Karlsen KH, Ohlberger M. . ‘A note on the uniqueness of entropy solutions of nonlinear degenerate parabolic equations.’ J. Math. Anal. Appl. 275: 439-458.

    • 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 and adaptive methods for convection dominated transport processes.
    • 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.
    • 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.

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

    • 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. . ‘Mixed finite element-finte volume methods for two-phase flow in porous media.’.
    • 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.
    • 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, 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, Rumpf M. . ‘Hierarchical and adaptive visualization on nested grids.’ Computing 59, No. Computing: 365 - 385.
    • 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.

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    Habilitations

    Henning, PatrickApplications of numerical homogenization in geosciences and physics
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    Dissertations

    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