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

G. R. Barrenechea (), V. John () and P. Knobloch ()
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G. R. Barrenechea: University of Strathclyde, Department of Mathematics and Statistics
V. John: Weierstrass Institute for Applied Analysis and Stochastics (WIAS)
P. Knobloch: Charles University, Department of Numerical Mathematics,Faculty of Mathematics and Physics

A chapter in Numerical Mathematics and Advanced Applications 2011, 2013, pp 237-245 from Springer

Abstract: 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.

Keywords: Finite Element Method; Interior Vertex; Finite Element Space; Spurious Oscillation; Continuous Piecewise Linear Function (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-33134-3_26

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DOI: 10.1007/978-3-642-33134-3_26

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