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A Nonlinear Local Projection Stabilization for Convection-Diffusion-Reaction Equations

In: Numerical Mathematics and Advanced Applications 2011

Author

Listed:
  • G. R. Barrenechea

    (University of Strathclyde, Department of Mathematics and Statistics)

  • V. John

    (Weierstrass Institute for Applied Analysis and Stochastics (WIAS)
    Free University of Berlin, Department of Mathematics and Computer Science)

  • P. Knobloch

    (Charles University, Department of Numerical Mathematics,Faculty of Mathematics and Physics)

Abstract

We propose a new local projection stabilization (LPS) finite element method for convection-diffusion-reaction equations. The discretization contains a crosswind diffusion term which depends on the unknown discrete solution in a nonlinear way. Consequently, the resulting method is nonlinear. Solvability of the nonlinear problem is established and an a priori error estimate in the LPS norm is proved. Numerical results show that the nonlinear crosswind diffusion term leads to a reduction of spurious oscillations.

Suggested Citation

  • G. R. Barrenechea & V. John & P. Knobloch, 2013. "A Nonlinear Local Projection Stabilization for Convection-Diffusion-Reaction Equations," Springer Books, in: Andrea Cangiani & Ruslan L. Davidchack & Emmanuil Georgoulis & Alexander N. Gorban & Jeremy Levesley (ed.), Numerical Mathematics and Advanced Applications 2011, edition 127, pages 237-245, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-33134-3_26
    DOI: 10.1007/978-3-642-33134-3_26
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