Mathematical Modeling and Analysis

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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