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Combined Nonconforming/Mixed-hybrid Finite Element-Finite Volume Scheme for Degenerate Parabolic Problems

In: Numerical Mathematics and Advanced Applications

Author

Listed:
  • Robert Eymard

    (Université de Marne-la-Vallée, Département de Mathématiques)

  • Danielle Hilhorst

    (Université de Paris-Sud et CNRS, Laboratoire de Mathématiques, Analyse Numérique et EDP)

  • Martin Vohralík

    (Université de Paris-Sud et CNRS, Laboratoire de Mathématiques, Analyse Numérique et EDP
    Czech Technical University in Prague, Department of Mathematics, Faculty of Nuclear Sciences and Physical Engineering)

Abstract

Summary We propose and analyze an efficient numerical scheme for nonlinear degenerate parabolic convection-reaction-diffusion equations. We discretize the diffusion term, which generally involves a full matrix diffusion tensor, by means of piecewise linear nonconforming (Crouzeix-Raviart) finite elements over a triangulation of the space domain, or using the stiffness matrix of the hybridization of the lowest order Raviart-Thomas mixed finite element method. The other terms are discretized by means of a finite volume scheme on a dual mesh, where the dual volumes are constructed around the sides of the original triangulation. Checking the local Peclet number, we set up the exact necessary amount of upstream weighting to avoid spurious oscillations in the velocity dominated case. Under the regularity condition for the triangulation, using a priori estimates and Kolmogorov’s relative compactness theorem, the convergence of the scheme is proved.

Suggested Citation

  • Robert Eymard & Danielle Hilhorst & Martin Vohralík, 2004. "Combined Nonconforming/Mixed-hybrid Finite Element-Finite Volume Scheme for Degenerate Parabolic Problems," Springer Books, in: Miloslav Feistauer & Vít Dolejší & Petr Knobloch & Karel Najzar (ed.), Numerical Mathematics and Advanced Applications, pages 288-297, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-18775-9_26
    DOI: 10.1007/978-3-642-18775-9_26
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