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Newton—Type Methods for the Mixed Finite Element Discretization of Some Degenerate Parabolic Equations

In: Numerical Mathematics and Advanced Applications

Author

Listed:
  • Florin A. Radu

    (University Erlangen-Nürnberg, Institute of Applied Mathematics)

  • Iuliu Sorin Pop

    (Technische Universiteit Eindhoven, CASA)

  • Peter Knabner

    (University Erlangen-Nürnberg, Institute of Applied Mathematics)

Abstract

In this paper we discuss some iterative approaches for solving the nonlinear algebraic systems encountered as fully discrete counterparts of some degenerate (fast diffusion) parabolic problems. After regularization, we combine a mixed finite element discretization with the Euler implicit scheme. For the resulting systems we discuss three iterative methods and give sufficient conditions for convergence.

Suggested Citation

  • Florin A. Radu & Iuliu Sorin Pop & Peter Knabner, 2006. "Newton—Type Methods for the Mixed Finite Element Discretization of Some Degenerate Parabolic Equations," Springer Books, in: Alfredo Bermúdez de Castro & Dolores Gómez & Peregrina Quintela & Pilar Salgado (ed.), Numerical Mathematics and Advanced Applications, pages 1192-1200, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-34288-5_120
    DOI: 10.1007/978-3-540-34288-5_120
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