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Angle Conditions for Discrete Maximum Principles in Higher-Order FEM

In: Numerical Mathematics and Advanced Applications 2009

Author

Listed:
  • Tomáš Vejchodský

    (Academy of Sciences, Institute of Mathematics)

Abstract

This contribution reviews the general theory of the discrete Green’s function and presents a numerical experiment indicating that the discrete maximum principle (DMP) fails to hold in the case of Poisson problem on any uniform triangulation of a triangular domain for orders of approximation three and higher. This extends the result [Computing 27, 145–154 (1981)] that the Laplace equation discretized by the higher-order FEM satisfies the DMP on a patch of triangular elements in exceptional cases only.

Suggested Citation

  • Tomáš Vejchodský, 2010. "Angle Conditions for Discrete Maximum Principles in Higher-Order FEM," Springer Books, in: Gunilla Kreiss & Per Lötstedt & Axel Målqvist & Maya Neytcheva (ed.), Numerical Mathematics and Advanced Applications 2009, pages 901-909, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-11795-4_97
    DOI: 10.1007/978-3-642-11795-4_97
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