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Discrete Maximum Principle for Galerkin Finite Element Solutions to Parabolic Problems on Rectangular Meshes

In: Numerical Mathematics and Advanced Applications

Author

Listed:
  • István Faragó

    (Eötvös Loränd University, Department of Applied Analysis)

  • Róbert Horváth

    (University of West-Hungary, Institute of Mathematics and Statistics)

  • Sergey Korotov

    (University of Jyväskylä, Department of Mathematical Information Technology)

Abstract

Summary One of the most important problems in numerical simulation is the preservation of qualitative properties of solutions of mathematical models. For problems of parabolic type, one of such properties is the maximum principle. In [5], Fujii analyzed the discrete analogue of the (continuous) maximum principle for the linear parabolic problems, and derived sufficient conditions guaranteeing its validity for the Galerkin finite element approximations built on simplicial meshes. In our paper, we present the sufficient conditions for the validity of the discrete maximum principle for the case of bilinear finite element space approximations on rectangular meshes.

Suggested Citation

  • István Faragó & Róbert Horváth & Sergey Korotov, 2004. "Discrete Maximum Principle for Galerkin Finite Element Solutions to Parabolic Problems on Rectangular Meshes," Springer Books, in: Miloslav Feistauer & Vít Dolejší & Petr Knobloch & Karel Najzar (ed.), Numerical Mathematics and Advanced Applications, pages 298-307, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-18775-9_27
    DOI: 10.1007/978-3-642-18775-9_27
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