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Mathematical Modeling and Analysis
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Markus Berndt
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Publications
2008
Markus Berndt, Glen Hansen and David Moulton, "
Efficient Nonlinear Solvers for Laplace-Beltrami Smoothing of Three-Dimensional Unstructured Grids
",
Computers & Mathematics with Applications
, vol. 55, pp. 2791-2806, 2008
2005
Markus Berndt, Konstantin Lipnikov, Pavel Vachal and Mikhail Shashkov, "
A Node Reconnection Algorithm for Mimetic Finite Difference Discretizations of Elliptic Equations on Triangular Meshes
",
Communications in Mathematical Sciences
, vol. 3, no. 4, pp. 665-680, 2005
Markus Berndt, Konstantin Lipnikov, Mikhail Shashkov, Mary F. Wheeler and Ivan Yotov, "
A Mortar Mimetic Finite Difference Method on Non-Matching Grids
",
Numerische Mathematik
, vol. 102, no. 2, pp. 203-230, 2005
Markus Berndt, Konstantin Lipnikov, Mikhail Shashkov, Mary F. Wheeler and Ivan Yotov, "
Superconvergence of the velocity in mimetic finite difference methods on quadrilaterals
",
SIAM J. Numer. Anal.
, vol. 43, no. 4, pp. 1728-1749, 2005
Markus Berndt, Thomas A. Manteuffel and Stephen F. McCormick, "
Analysis of First-Order System Least Squares (FOSLS) for Elliptic Problems with Discontinuous Coefficients: Part II
",
SIAM J. Numer. Anal.
, vol. 43, no. 1, pp. 409-436, 2005
Markus Berndt, Thomas A. Manteuffel, Stephen F. McCormick and Gerhard Starke, "
Analysis of First-Order System Least Squares (FOSLS) for Elliptic Problems with Discontinuous Coefficients: Part I
",
SIAM J. Numer. Anal.
, vol. 43, no. 1, pp. 386-408, 2005
2004
Travis Austin, Markus Berndt and David Moulton, "
A memory efficient parallel tridiagonal solver
", Preprint LA-UR-03-4149, 2004
2003
Markus Berndt and Mikhail Shashkov, "
Multilevel Accelerated Optimization for Problems in Grid Generation
", in
Proceedings of the 12th International Meshing Roundtable
, (Santa Fe, NM), 2003
2001
Markus Berndt, Konstantin Lipnikov, J. David Moulton and Mikhail Shashkov, "
Convergence of mimetic finite difference discretizations
",
East-West Journal of Numerical Mathematics
, vol. 9, no. 4, pp. 265--284, 2001
1999
Markus Berndt,
Adaptive Refinement and the Treatment of Discontinuous Coefficients for Multilevel First-Order System Least Squares
, PhD thesis, University of Colorado, 1999
1997
Markus Berndt, Thomas A. Manteuffel and Stephen F. McCormick, "
Local error estimates and adaptive refinement for first-order system least squares (FOSLS)
",
E.T.N.A.
, vol. 6, pp. 35-43, 1997
Daniel Quinlan and Markus Berndt, "
MLB: Multilevel load balancing for structured grid applications
", in
Proceedings of the SIAM Parallel Conference
, (Minneapolis, MN), 1997
1996
Markus Berndt and Kristian Witsch, "
Multigrid on overlapping patches
", in
Proceedings of the Seventh Copper Mountain Conference on Multigrid Methods, volume CP 3339
, (NASA, Hampton, VA), pp. 31-40, 1996
1994
Markus Berndt,
Multi-Level Verfahren und adaptive Verfeinerungen
, Diplom thesis, Heinrich Heine Universität Düsseldorf, 1994