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G. Matthies, L. Tobiska
A two-level local projection stabilisation on uniformly
refined triangular meshes
Numer. Algorithms, 61 (2012), pp. 465-478.
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N. Ahmed, G. Matthies
Numerical studies of variational-type time-discretization
techniques for transient Oseen problems
in: ALGORITMY 2012, 19th Conference on Scientific
Computing,
A. Handlovicova, Z. Minarechova, D. Sevcovic,
Slovak University of Technology, Bratislava, 2012, pp. 404-415.
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N. Ahmed, G. Matthies
Numerical Studies of Galerkin-type Time-Discretizations
Applied to Transient Convection-Diffusion-Reaction
Equations
World Acad. Sci. Eng. Tech., 66 (2012), pp. 586-593.
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N. Ahmed, G. Matthies, L. Tobiska
Finite element methods of an operator splitting applied to population
balance equations
J. Comput. Appl. Math., 236 (2011), pp. 1604-1621.
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S. Franz, G. Matthies
Local Projection Stabilisation on Layer-Adapted Meshes for
Convection-Diffusion Problems with Characteristic Layers
(Part I and II)
in: BAIL 2010 - Boundary and Interior Layers, Computational and
Asymptotic Methods,
ed. by C. Clavero, J. L. Gracia, F. J. Lisbona,
vol. 81 of Lecture Notes in Computational Science and
Engineering, Springer-Verlag 2011, pp. 127-138.
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N. Ahmed, G. Matthies, L. Tobiska, H. Xie
Discontinuous Galerkin time stepping with local projection
stabilization for transient
convection-diffusion-reaction problems
Comput. Methods Appl. Mech. Engrg., 200 (2011), pp. 1747-1756.
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S. Franz, G. Matthies
Convergence on Layer-Adapted Meshes and Anisotropic Interpolation
Error Estimates of Non-Standard Higher Order Finite Elements
Appl. Numer. Math., 61 (2011), pp. 723-737.
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S. Franz, G. Matthies
Local projection stabilisation on S-type meshes for
convection-diffusion problems with characteristic layers
Computing, 87 (2010), pp. 135-167.
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G. Matthies, G. Lube, L. Röhe
Some remarks on residual-based stabilisation of inf-sup stable
discretisations of the generalised Oseen problem
Comput. Methods Appl. Math., 9 (2009), pp. 368-390.
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G. Matthies
Local projection methods on layer-adapted meshes for higher
order discretisations of convection-diffusion problems
Appl. Numer. Math., 59 (2009), pp. 2515-2533.
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G. Matthies
Local projection stabilisation for higher order discretisations
of convection-diffusion problems on Shishkin meshes
Adv. Comput. Math., 30 (2009), pp. 315-337.
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G. Matthies, P. Skrzypacz, L. Tobiska
Stabilisation of local projection type applied to
convection-diffusion problems with mixed boundary conditions
Electron. Trans. Numer. Anal., 32 (2008), pp. 90-105.
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A. Linke, G. Matthies, L. Tobiska
Non-Nested Multi-Grid Solvers for Mixed Divergence-free
Scott-Vogelius Discretizations
Computing, 83 (2008), pp. 87-107.
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L. Tobiska, G. Matthies
A Numerical Study of Local Projection
Stabilisation Applied to Oseen Problems
in: Numerical Mathematics and Advanced Applications,
Proceedings of ENUMATH 2007, the 7th European Conference on
Numerical Mathematics and Advanced Applications, Graz, Austria,
September 2007,
ed. by K. Kunisch, G. Of and O. Steinbach,
Springer-Verlag Berlin Heidelberg, 2008, pp. 489-496.
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S. Ganesan, G. Matthies, L. Tobiska
Local projection stabilization of equal order interpolation
applied to the Stokes problem
Math. Comp., 77 (2008), pp. 2039-2060
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G. Matthies, F. Schieweck
Nonconforming finite elements of higher order
satisfying a new compatibility condition
J. Numer. Math., 16 (2008), pp. 23-50
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Th. Apel, G. Matthies
Nonconforming, anisotropic, rectangular finite elements of arbitrary
order for the Stokes problem
SIAM J. Numer. Anal., 46 (2008), pp. 1867-1891
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O. Lavrova, G. Matthies, L. Tobiska
Numerical study of soliton-like surface configurations on a
magnetic fluid layer in the Rosensweig instability
Commun. Nonlinear Sci. Numer. Simul., 13 (2008), pp. 1302-1310.
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H. Knieling, A. Lange, G. Matthies, I. Rehberg,
R. Richter
Maximal growth rate at the Rosensweig instability: theory,
experiment, and numerics
Proc. Appl. Math. Mech., 7 (2007), pp. 4140025-4140026.
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G. Matthies, L. Tobiska
Mass conservation of finite element methods for coupled
flow-transport problems
Int. J. Computing Science and Mathematics, 1 (2007), pp. 293-307.
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H. Knieling, R. Richter, I. Rehberg, G. Matthies,
A. Lange
Growth of surface undulations at the Rosensweig instability
Phys. Rev. E., 76 (2007), 066301.
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L. P. Franca, V. John, G. Matthies, L. Tobiska
An inf-sup stable and residual-free bubble element for the Oseen
equations
SIAM J. Numer. Anal., 45 (2007), pp. 2392-2407.
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G. Matthies
Inf-sup stable nonconforming finite elements of higher order on
quadrilaterals and hexahedra
M2AN Math. Model. Numer. Anal., 41 (2007), pp. 855-874.
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G. Matthies, P. Skrzypacz, L. Tobiska
A unified convergence analysis for local projection stabilisations
applied to the Oseen problem
M2AN Math. Model. Numer. Anal., 41 (2007), pp. 713-742.
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G. Matthies, F. Schieweck
On the reference mapping for quadrilateral and hexahedral
finite elements on multilevel adaptive grids
Computing, 80 (2007), pp. 95-119.
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Chr. Gollwitzer, G. Matthies, R. Richter,
I. Rehberg, L. Tobiska
The surface topography of a magnetic fluid: a quantitative
comparison between experiment and numerical simulation
J. Fluid Mech. 571 (2007), pp. 455-474.
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S. Ganesan, G. Matthies, L. Tobiska
On spurious velocities in incompressible flow problems with interfaces
Comput. Methods Appl. Mech. Engrg. 196 (2007), pp. 1193-1202.
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O. Lavrova, G. Matthies, T. Mitkova, V. Polevikov,
L. Tobiska
Numerical treatment of free surface problems in ferrohydrodynamics
J. Phys.: Condens. Matter 18 (2006), pp. 2657-2669.
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V. John, G. Matthies, J. Rang
A comparison of time-discretization/linearization
approaches for the incompressible Navier-Stokes equations
Comput. Methods Appl. Mech. Engrg. 195 (2006), pp. 5995-6010.
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G. Matthies, F. Schieweck
A Multigrid Method for Incompressible Flow Problems Using Quasi
Divergence Free Functions
SIAM J Sci. Comput., 28 (2006), pp. 141-171.
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G. Matthies, L. Tobiska
Inf-sup stable non-conforming finite elements of
arbitrary order on triangles
Numer. Math., 102 (2005), pp. 293-309.
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G. Matthies, P. Skrzypacz, L. Tobiska
Superconvergence of a 3d finite element method for stationary
Stokes and Navier-Stokes problems
Numer. Meth. Part. Diff. Eq., 21 (2005), pp. 701-725.
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G. Matthies, L. Tobiska
Numerical simulation of normal-field instability in the static
and dynamic case
J. Magn. Magn. Mater., 289 (2005), pp. 346-349.
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G. Matthies, O. Lavrova, L. Tobiska
Numerical simulation of the Rosensweig instability
of ferrorfluids in the static and dynamic case
Oberwolfach Rep., 2 (2005), pp. 483-485.
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O. Lavrova, G. Matthies, V. Polevikov, L. Tobiska
Numerical modeling of the equilibrium shapes
of a ferrofluid drop in an external magnetic
field
Proc. Appl. Math. Mech., 4 (2004), pp. 704-705.
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V. John, G. Matthies
MooNMD - a program package based on mapped
finite element methods
Comput. Vis. Sci., 6 (2004), pp. 163-170.
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U. Krewer, Y. Song, K. Sundmacher;
V. John, R. Lübke, G. Matthies, L. Tobiska
Direct methanol fuel cell (DMFC): analysis of residence
time behaviour of anodic flow bed
Chemical Engineering Science, 59 (2003), pp. 119-130.
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O. Lavrova, G. Matthies, T. Mitkova,
V. Polevikov, L. Tobiska
Finite Element Methods for Coupled Problems in
Ferrohydrodynamics
in: Challenges in Scientific Computing - CISC 2002,
Proceedings of the Conference "Challenges in Scientific
Computing", Berlin, Oct 2-5, 2002,
ed. by E. Bänsch,
vol. 35 of Lecture Notes in Computational Science and
Engineering, Springer-Verlag 2003, pp. 160-183.
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T. Iliescu, V. John, W. J. Layton,
G. Matthies, L. Tobiska
A Numerical Study of a Class of LES Models
Int. J. Comput. Fluid Dyn., 17 (2003), pp. 75-85.
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G. Matthies, L. Tobiska
Finite Element Simulations of Magnetic Liquids with
Free Boundary
Proc. Appl. Math. Mech., 1 (2002), pp. 319-320.
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G. Matthies, L. Tobiska
The inf-sup condition for the mapped
Qk/Pk-1disc element
in arbitrary space dimensions
Computing, 69 (2002), pp. 119-139.
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J. John, P. Knobloch, G. Matthies,
L. Tobiska
Non-nested Multi-level Solvers for Finite Element
Discretisations of Mixed Problems
Computing, 68 (2002), pp. 313-341.
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V. John, G. Matthies
Higher Order Finite Element Discretizations in a
Benchmark Problem for Incompressible Flows
Int. J. Num. Meth. Fluids, 37 (2001), pp. 885-903.
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G. Matthies
Mapped Finite Elements on Hexahedra. Necessary and
Sufficient Conditions for Optimal Interpolation Errors
Numer. Algorithms, 27 (2001), pp. 317-327.
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G. Matthies, L. Tobiska
The Streamline-Diffusion Method for Conforming and
Nonconforming Finite Elements of lowest Order applied to
Convection-Diffusion Problems
Computing, 66 (2001), pp. 343-364.
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G. Matthies
Numerische Lösung der Navier-Stokes-Gleichungen in
Gebieten mit bewegtem Rand
Technische Mechanik 20 (2000), pp. 195-204.
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V. John, G. Matthies, F. Schieweck,
L. Tobiska
A streamline-diffusion method for
nonconforming finite element approximations applied to
convection-diffusion problems
Comput. Methods Appl. Mech. Engrg. 166 (1998), pp. 85-97.
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G. Matthies
Mathematische Untersuchung des Verhaltens von
magnetischen Flüssigkeiten
in: Preprint MBI-99-1 (Workshop Gommern 1998) des
Graduiertenkolleg "Modellierung, Berechnung und
Identifikation mechanischer Systeme", 1999,
pp. 39-44.
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V. John, G. Matthies, T.I. Mitkova,
L. Tobiska, P.S. Vassilevski
A Comparison of Three Solvers for the Incompressible
Navier-Stokes Equations
in: Large-Scale Scientific Computations of Engineering and
Environmental Problems,
ed. by M. Griebel, S. Margenov, and P. Yalamov,
vol. 73 of Notes on Numerical Fluid Mechanics,
Vieweg, Braunschweig, 2000, pp. 215-222.
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L. Tobiska, G. Matthies, M. Stynes
Convergence Properties of the
Streamline-Diffusion Finite Element Method on a Shishkin Mesh
for Singularly Perturbed Elliptic Equations with Exponential
Layers
in: Analytical and Numerical Methods for Convection-Dominated
and Singularly Perturbed Problems,
ed. by L. G. Vulkov, J. J. H. Miller, and G. I. Shishkin,
Nova Science Publishers, Inc., New York, 2000, pp. 23-132.
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G. Matthies, L. Tobiska
Simulation of free surfaces of magnetic liquids
in: ALGORITMY 2000, 15th Conference on Scientific
Computing,
ed. by A. Handlovicova, M. Komornikova, K. Mikula,
D. Sevcovic,
Slovak University of Technology, Bratislava, 2000, pp. 1-10.
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G. Matthies, L. Tobiska
Finite Element Discretization for Ferrofluids
in: Proceedings of Fourth International pamir Conference on
Magnetohydrodynamics,
Presqu'ile de Giens, 2000, pp. 787-792.
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G. Matthies, L. Tobiska
Adaptive and Higher Order Finite Elements for
Three-Dimensional Magnetic Field Calculations in
Ferrohydrodynamics
in: Proceedings of the 9th International Conference on
Magnetic Fluids, Bremen, 2001.
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V. John, G. Matthies, L. Tobiska
On Higher Order Finite Element Discretizations for
the Incompressible Navier-Stokes Equations in Three
Dimensions
in: Proceedings of ECCOMAS CFD 2001, Swansea, 2001.
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G. Matthies, L. Tobiska
Mass conservation of finite element methods for coupled
flow-transport problems
Proceedings of the International Conference on Boundary and Interior
Layers BAIL 2006, G. Lube and G. Rapin, eds., 2006.
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