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

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Numerical Mathematics and Advanced Applications 2009

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.

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References

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Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, Helmut Schmidt University, University of the Federal Armed Forces Hamburg, Holstenhofweg 85, 22043, Hamburg, Germany

    Markus Bause

Authors
  1. Markus Bause
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Correspondence to Markus Bause .

Editor information

Editors and Affiliations

  1. Dept. of Information Technology, Uppsala University, Uppsala, 751 05, Sweden

    Gunilla Kreiss

  2. Dept. of Information Technology, Uppsala University, Uppsala, 751 05, Sweden

    Per Lötstedt

  3. Dept. of Information Technology, Uppsala University, Uppsala, 751 05, Sweden

    Axel Målqvist

  4. Dept. of Information Technology, Uppsala University, Uppsala, 751 05, Sweden

    Maya Neytcheva

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Bause, M. (2010). Stabilized Finite Element Methods with Shock-Capturing for Nonlinear Convection–Diffusion-Reaction Models. In: Kreiss, G., Lötstedt, P., Målqvist, A., Neytcheva, M. (eds) Numerical Mathematics and Advanced Applications 2009. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11795-4_12

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