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Stabilized Finite Element Methods with Shock-Capturing for Nonlinear Convection–Diffusion-Reaction Models

In: Numerical Mathematics and Advanced Applications 2009

Author

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  • Markus Bause

    (Helmut Schmidt University, University of the Federal Armed Forces Hamburg, Department of Mechanical Engineering)

Abstract

In this work stabilized higher-order finite element approximations of convection-diffusion-reactions models with nonlinear reaction mechanisms are studied. Streamline upwind Petrov–Galerkin (SUPG) stabilization together with anisotropic shock-capturing as an additional stabilization in crosswind-direction is used. The parameter design of the scheme is described precisely and error estimates are provided. Theoretical results are illustrated by numerical computations. The work extends former investigations for linear problems to more realistic nonlinear models.

Suggested Citation

  • Markus Bause, 2010. "Stabilized Finite Element Methods with Shock-Capturing for Nonlinear Convection–Diffusion-Reaction Models," Springer Books, in: Gunilla Kreiss & Per Lötstedt & Axel Målqvist & Maya Neytcheva (ed.), Numerical Mathematics and Advanced Applications 2009, pages 125-133, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-11795-4_12
    DOI: 10.1007/978-3-642-11795-4_12
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