Publications

  • Simon Becher, Gunar Matthies: Unified analysis for variational time discretizations of higher order and higher regularity applied to non-stiff ODEs, Numer. Algorithms, 89
    1533––1565, 2022.
    https://doi.org/10.1007/s11075-021-01164-z
  • Naveed Ahmed, Gunar Matthies: Higher-order discontinuous Galerkin time discretizations for the evolutionary Navier–Stokes equations, IMA J. Numer. Anal., 41, 3113–3144, 2021.
    https://doi.org/10.1093/imanum/draa053
  • Simon Becher, Gunar Matthies: Variational time discretizations of higher order and higher regularity, BIT Numer. Math., 61, 721-755, 2021.
    https://doi.org/10.1007/s10543-021-00851-6
  • Mathias Anselmann, Markus Bause, Simon Becher, Gunar Matthies: Galerkin-collocation approximation in time for the wave equation and its post-processing, M2AN Math. Model. Numer. Anal., 54, 2099-2123, 2020.
    https://doi.org/10.1051/m2an/2020033
  • Simon Becher, Gunar Matthies, Dennis Wenzel: Variational Methods for Stable Time Discretization of First-Order Differential Equations, in: Advanced Computing in Industrial Mathematics: BGSIAM 2017, (Eds.: Krassimir Georgiev, Michail Todorov, Ivan Georgiev), vol. 793 of Studies in Computational Intelligence, Springer International Publishing, 63-75, 2019.
    https://dx.doi.org/10.1007/978-3-319-97277-0_6
  • Sebastian Franz, Gunar Matthies: A unified framework for time-dependent singularly perturbed problems with discontinuous Galerkin methods in time, Math. Comp., 87, 2113-2132, 2018.
    https://dx.doi.org/10.1090/mcom/3326
  • Sebastian Franz, Katharina Höhne, Gunar Matthies: Grad-div stabilized discretizations on S-type meshes for the Oseen problem, IMA J. Numer. Anal., 38, 299-329, 2018.
    https://dx.doi.org/10.1093/imanum/drw069
  • Naveed Ahmed, Volker John, Gunar Matthies, Julia Novo: A local projection stabilization/continuous Galerkin–Petrov method for incompressible flow problems, Appl. Math. Comput., 333, 304-324, 2018.
    https://dx.doi.org/10.1016/j.amc.2018.03.088

  • Naveed Ahmed, Gunar Matthies: Numerical studies of higher order variational time stepping schemes for evolutionary Navier-Stokes equations, in: Boundary and Interior Layers, Computational and Asymptotic Methods - BAIL 2016 (Eds.: Zhongyi Huang, Martin Stynes, Zhimin Zhang), vol. 120 of Lecture Notes in Computational Science and Engineering, Springer-Verlag, 19-33, 2017.
    https://dx.doi.org/10.1007/978-3-319-67202-1

  • Ulrich Wilbrandt, Clemens Bartsch, Naveed Ahmed, Najib Alia, Felix Anker, Laura Blank, Alfonso Caiazzo, Sashikumaar Ganesan, Swetlana Giere, Gunar Matthies, Raviteja Meesala, Abdus Shamim, Jagannath Venkatesan, Volker John: ParMooN - A modernized program package based on mapped finite elements,  Comput. Math. Appl., 74, 74-88, 2017.
    https://dx.doi.org/10.1016/j.camwa.2016.12.020

  •  Naveed Ahmed, Simon Becher, Gunar Matthies: Higher-order discontinuous Galerkin time stepping and local projection stabilization techniques for the transient Stokes problem, Comput. Methods Appl. Mech. Engrg., 313, 28-52, 2017.
    https://dx.doi.org/10.1016/j.cma.2016.09.026

  • Gunar Matthies, Mehdi Salimi, Somayeh Sharifi, Juan Luis Varona: An optimal three-point eighth-order iterative method without memory for solving nonlinear equations with its dynamics, Jpn. J. Ind. Appl. Math., 33, 751-766, 2016.
    https://dx.doi.org/10.1007/s13160-016-0229-5

  • Naveed Ahmed, Gunar Matthies: Numerical Study of SUPG and LPS Methods Combined with Higher Order Variational Time Discretization Schemes Applied to Time-Dependent Linear Convection–Diffusion–Reaction Equations, J. Sci. Comput., 67, 988-1018, 2016.
    https://dx.doi.org/10.1007/s10915-015-0115-3

  • Alexander Linke, Gunar Matthies, Lutz Tobiska: Robust Arbitrary Order Mixed Finite Element Methods for the Incompressible Stokes Equations with pressure independent velocity errors, M2AN Math. Model. Numer. Anal., 50, 289-309, 2016.
    https://dx.doi.org/10.1051/m2an/2015044

  • Naveed Ahmed, Gunar Matthies: Higher order continuous Galerkin-Petrov time stepping schemes for transient convection-diffusion-reaction equations,  M2AN Math. Model. Numer. Anal., 49, 1429-1450, 2015.
    https://dx.doi.org/10.1051/m2an/2015019

  • Gunar Matthies, Lutz Tobiska: Local projection type stabilization applied to inf–sup stable discretizations of the Oseen problem,  IMA J. Numer. Anal., 35, 239-269, 2015.
    https://dx.doi.org/10.1093/imanum/drt064

  • Naveed Ahmed, Gunar Matthies, Lutz Tobiska: Stabilized finite element discretization applied to an operator-splitting method of population balance equations, Appl. Numer. Math., 70, 58-79, 2013.
    https://dx.doi.org/10.1016/j.apnum.2013.04.001

  • Gunar Matthies, Lutz Tobiska: A two-level local projection stabilisation on uniformly refined triangular meshes, Numer. Algorithms, 61, 465-478, 2012.
    https://dx.doi.org/10.1007/s11075-012-9543-4

  • Naveed Ahmed, Gunar Matthies: Numerical Studies of Galerkin-type Time-Discretizations Applied to Transient Convection-Diffusion-Reaction Equations, World Acad. Sci. Eng. Tech., 66, 586-593, 2012.
    https://scholar.waset.org/1307-6892/1200

  • Naveed Ahmed, Gunar Matthies, Lutz Tobiska: Finite element methods of an operator splitting applied to population balance equations, J. Comput. Appl. Math., 236, 1604-1621, 2011.
    https://dx.doi.org/10.1016/j.cam.2011.09.025

  • Naveed Ahmed, Gunar Matthies, Lutz Tobiska, Hehu Xie: Discontinuous Galerkin time stepping with local projection stabilization for transient convection-diffusion-reaction problems, Comput. Methods Appl. Mech. Engrg., 200, 1747-1756, 2011.
    https://dx.doi.org/10.1016/j.cma.2011.02.003

  • Sebastian Franz, Gunar Matthies: Convergence on Layer-Adapted Meshes and Anisotropic Interpolation Error Estimates of Non-Standard Higher Order Finite Elements, Appl. Numer. Math., 61, 723-737, 2011.
    https://dx.doi.org/10.1016/j.apnum.2011.02.001

  • Sebastian Franz, Gunar Matthies: Local projection stabilisation on S-type meshes for convection-diffusion problems with characteristic layers, Computing, 87, 135-167, 2010.
    https://dx.doi.org/10.1007/s00607-010-0079-y

  • Gunar Matthies, Gert Lube, Lars Röhe: Some remarks on residual-based stabilisation of inf-sup stable discretisations of the generalised Oseen problem, Comput. Methods Appl. Math., 9, 368-390, 2009.
    https://dx.doi.org/10.2478/cmam-2009-0024

  • Gunar Matthies: Local projection methods on layer-adapted meshes for higher order discretisations of convection-diffusion problems, Appl. Numer. Math., 59, 2515-2533, 2009.
    https://dx.doi.org/10.1016/j.apnum.2009.05.008

  • Gunar Matthies: Local projection stabilisation for higher order discretisations of convection-diffusion problems on Shishkin meshes, Adv. Comput. Math., 30, 315-337, 2009.
    https://dx.doi.org/10.1007/s10444-008-9070-y

  • Gunar Matthies, Piotr Skrzypacz, Lutz Tobiska: Stabilization of local projection type applied to convection-diffusion problems with mixed boundary conditions, Electron. Trans. Numer. Anal., 32, 90-105, 2008.
    http://etna.mcs.kent.edu/vol.32.2008/pp90-105.dir/pp90-105.html

  • Alexander Linke, Gunar Matthies, Lutz Tobiska: Non-Nested Multi-Grid Solvers for Mixed Divergence-free Scott-Vogelius Discretizations, Computing, 83, 87-107, 2008.
    https://dx.doi.org/10.1007/s00607-008-0016-5

  • Sashikumaar Ganesan, Gunar Matthies, Lutz Tobiska: Local projection stabilization of equal order interpolation applied to the Stokes problem, Math. Comp., 77, 2008, 2039-2060.
    https://dx.doi.org/10.1090/S0025-5718-08-02130-3

  • Gunar Matthies, Friedhelm Schieweck: Nonconforming finite elements of higher order satisfying a new compatibility condition, J. Numer. Math., 16, 23-50, 2008.
    https://dx.doi.org/10.1515/JNUM.2008.002

  • Thomas Apel, Gunar Matthies: Nonconforming, anisotropic, rectangular finite elements of arbitrary order for the Stokes problem, SIAM J. Numer. Anal., 46, 1867-1891, 2008.
    https://dx.doi.org/10.1137/060666652

  • Olga Lavrova, Gunar Matthies, Lutz Tobiska: Numerical study of soliton-like surface configurations on a magnetic fluid layer in the Rosensweig instability, Commun. Nonlinear Sci. Numer. Simul., 13, 1302-1310, 2008.
    https://dx.doi.org/10.1016/j.cnsns.2006.12.006

  • Holger Knieling, Adrian Lange, Gunar Matthies, Ingo Rehberg, Reinhard Richter: Maximal growth rate at the Rosensweig instability: theory, experiment, and numerics, Proc. Appl. Math. Mech., 7, 4140025-4140026, 2007.
    https://dx.doi.org/10.1002/pamm.200700969

  • Gunar Matthies, Lutz Tobiska: Mass conservation of finite element methods for coupled flow-transport problems, Int. J. Comput. Sci. Math., 1, 293-307, 2007.
    https://dx.doi.org/10.1504/IJCSM.2007.016537

  • Holger Knieling, Reinhard Richter, Ingo Rehberg, Gunar Matthies, Adrian Lange: Growth of surface undulations at the Rosensweig instability, Phys. Rev. E, 76, 066301, 2007.
    https://dx.doi.org/10.1103/PhysRevE.76.066301

  • Leopoldo P. Franca, Volker John, Gunar Matthies, Lutz Tobiska: An inf-sup stable and residual-free bubble element for the Oseen equations, SIAM J. Numer. Anal., 45, 2392-2407, 2007.
    https://dx.doi.org/10.1137/060661454

  • Gunar Matthies: Inf-sup stable nonconforming finite elements of higher order on quadrilaterals and hexahedra, M2AN Math. Model. Numer. Anal., 41, 855-874, 2007.
    https://dx.doi.org/10.1051/m2an:2007034

  • Gunar Matthies, Piotr Skrzypacz, Lutz Tobiska: A unified convergence analysis for local projection stabilisations applied to the Oseen problem, M2AN Math. Model. Numer. Anal., 41, 713-742, 2007.
    https://dx.doi.org/10.1051/m2an:2007038

  • Gunar Matthies, Friedhelm Schieweck: On the reference mapping for quadrilateral and hexahedral finite elements on multilevel adaptive grids, Computing, 80, 95-119, 2007.
    https://dx.doi.org/10.1007/s00607-007-0228-0

  • Christian Gollwitzer, Gunar Matthies, Reinhard Richter, Ingo Rehberg, Lutz Tobiska: The surface topography of a magnetic fluid: a quantitative comparison between experiment and numerical simulation, J. Fluid Mech., 571, 455-474, 2007.
    https://dx.doi.org/10.1017/S0022112006003466

  • Sashikumaar Ganesan, Gunar Matthies, Lutz Tobiska: On spurious velocities in incompressible flow problems with interfaces, Comput. Methods Appl. Mech. Engrg., 196, 1193-1202, 2007.
    https://dx.doi.org/10.1016/j.cma.2006.08.018

  • Olga Lavrova, Gunar Matthies, Teodora Mitkova, Viktor Polevikov, Lutz Tobiska: Numerical treatment of free surface problems in ferrohydrodynamics, J. Phys.: Condens. Matter, 18, 2657-2669, 2006.
    https://dx.doi.org/10.1088/0953-8984/18/38/S09

  • Volker John, Gunar Matthies, Joachim Rang: A comparison of time-discretization/linearization approaches for the incompressible Navier-Stokes equations, Comput. Methods Appl. Mech. Engrg., 195, 5995-6010, 2006.
    https://dx.doi.org/10.1016/j.cma.2005.10.007

  • Gunar Matthies, Friedhelm Schieweck: A Multigrid Method for Incompressible Flow Problems Using Quasi Divergence Free Functions, SIAM J. Sci. Comput., 28, 141-171, 2006.
    https://dx.doi.org/10.1137/04061814X

  • Gunar Matthies, Lutz Tobiska: Inf-sup stable non-conforming finite elements of arbitrary order on triangles, Numer. Math., 102, 293-309, 2005.
    https://dx.doi.org/10.1007/s00211-005-0648-8

  • Gunar Matthies, Piotr Skrzypacz, Lutz Tobiska: Superconvergence of a 3D finite element method for stationary Stokes and Navier-Stokes problems, Num. Meth. Part. Diff. Equ., 21, 701-725, 2005.
    https://dx.doi.org/10.1002/num.20058

  • Gunar Matthies, Lutz Tobiska: Numerical simulation of normal-field instability in the static and dynamic case, J. Magn. Magn. Mater., 289, 346-349, 2005.
    https://dx.doi.org/10.1016/j.jmmm.2004.11.098

  • Olga Lavrova, Gunar Matthies, Viktor Polevikov, Lutz Tobiska: Numerical modeling of the equilibrium shapes of a ferrofluid drop in an external magnetic field, Proc. Appl. Math. Mech., 4, 704-705, 2004.
    https://dx.doi.org/10.1002/pamm.200410333

  • Volker John, Gunar Matthies: MooNMD - a program package based on mapped finite element methods, Comput. Vis. Sci., 6, 163-170, 2004.
    https://dx.doi.org/10.1007/s00791-003-0120-1

  • Ulrike Krewer, Y. Song, Kai Sundmacher, Volker John, Robert Lüke, Gunar Matthies, Lutz Tobiska: Direct methanol fuel cell (DMFC): analysis of residence time behaviour of anodic flow bed, Chem. Eng. Sci., 59, 119-130, 2004.
    https://dx.doi.org/10.1016/j.ces.2003.09.029

  • Traian Iliescu, Volker John, William J. Layton, Gunar Matthies, Lutz Tobiska: A Numerical Study of a Class of LES Models, Int. J. Comput. Fluid Dyn., 17, 75-85, 2003.
    https://dx.doi.org/10.1080/1061856021000009209

  • Gunar Matthies, Lutz Tobiska: Finite Element Simulations of Magnetic Liquids with Free Boundary, Proc. Appl. Math. Mech., 1, 319-320, 2002.
    https://dx.doi.org/10.1002/1617-7061(200203)1:1<319::AID-PAMM319>3.0.CO;2-3

  • Gunar Matthies, Lutz Tobiska: The Inf-Sup Condition for the Mapped Qk/Pk-1disc Element in Arbitrary Space Dimensions, Computing, 69, 119-139, 2002.
    https://dx.doi.org/10.1007/s00607-002-1451-3

  • Volker John, Petr Knobloch, Gunar Matthies, Lutz Tobiska: Non-nested Multi-level Solvers for Finite Element Discretisations of Mixed Problems, Computing, 68, 313-341, 2002.
    https://dx.doi.org/10.1007/s00607-002-1444-2

  • Gunar Matthies: Mapped finite elements on hexahedra. Necessary and sufficient conditions for optimal interpolation errors, Numer. Algorithms, 27, 317-327, 2001.
    https://dx.doi.org/10.1023/A:1013860707381

  • Gunar Matthies: Numerische Lösung der Navier-Stokes-Gleichungen in Gebieten mit bewegtem Rand, Technische Mechanik, 20, 195-204, 2000.
    http://www.uni-magdeburg.de/ifme/zeitschrift_tm/2000_Heft3/Matthies.pdf

  • Volker John, Gunar Matthies: Higher-order finite element discretizations in a benchmark problem for incompressible flows, Internat. J. Numer. Methods Fluids, 37, 885-903, 2001.
    https://dx.doi.org/10.1002/fld.195

  • Gunar Matthies, Lutz Tobiska: The Streamline-Diffusion Method for Conforming and Nonconforming Finite Elements of Lowest Order Applied to Convection-Diffusion Problems, Computing, 66, 343-364, 2001.
    https://dx.doi.org/10.1007/s006070170019

  • Volker John, Gunar Matthies, Friedhelm Schieweck, Lutz Tobiska: A streamline-diffusion method for nonconforming finite element approximations applied to convection-diffusion problems, Comput. Methods Appl. Mech. Engrg., 166, 85-97, 1998.
    https://dx.doi.org/10.1016/S0045-7825(98)80014-5

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Gunar Matthies
Last modified: Feb 21, 2024