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A local projection stabilization finite element method with nonlinear crosswind diffusion for convection-diffusion-reaction equations

Published online by Cambridge University Press:  30 July 2013

Gabriel R. Barrenechea ,
Volker John  and
Petr Knobloch
Gabriel R. Barrenechea
Affiliation:
Department of Mathematics and Statistics, University of Strathclyde, 26 Richmond Street, Glasgow G1 1XH, Scotland. gabriel.barrenechea@strath.ac.uk
Volker John
Affiliation:
Weierstrass Institute for Applied Analysis and Stochastics (WIAS), Mohrenstr. 39, 10117 Berlin, Germany and Free University of Berlin, Department of Mathematics and Computer Science, Arnimallee 6, 14195 Berlin, Germany; john@wias-berlin.de
Petr Knobloch
Affiliation:
Department of Numerical Mathematics, Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 18675 Praha 8, Czech Republic; knobloch@karlin.mff.cuni.cz
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Abstract

An extension of the local projection stabilization (LPS) finite element method for convection-diffusion-reaction equations is presented and analyzed, both in the steady-state and the transient setting. In addition to the standard LPS method, a nonlinear crosswind diffusion term is introduced that accounts for the reduction of spurious oscillations. The existence of a solution can be proved and, depending on the choice of the stabilization parameter, also its uniqueness. Error estimates are derived which are supported by numerical studies. These studies demonstrate also the reduction of the spurious oscillations.

Keywords

Finite element methodlocal projection stabilizationcrosswind diffusionconvection-diffusion-reaction equationwell posednesstime dependent problemstabilityerror estimates
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 47 , Issue 5 , September 2013 , pp. 1335 - 1366
Copyright
© EDP Sciences, SMAI, 2013

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