Volume 47, Number 5, September-October 2013
|Page(s)||1335 - 1366|
|Published online||30 July 2013|
A local projection stabilization finite element method with nonlinear crosswind diffusion for convection-diffusion-reaction equations
1 Department of Mathematics and Statistics, University of Strathclyde, 26 Richmond Street, Glasgow G1 1XH, Scotland
2 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
3 Department of Numerical Mathematics, Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 18675 Praha 8, Czech Republic
Received: 30 October 2012
Revised: 8 February 2013
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.
Mathematics Subject Classification: 65N30 / 65N12 / 65N15 / 65M60
Key words: Finite element method / local projection stabilization / crosswind diffusion / convection-diffusion-reaction equation / well posedness / time dependent problem / stability / error estimates
© EDP Sciences, SMAI, 2013
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