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.
@article{M2AN_2013__47_5_1335_0,
author = {Barrenechea, Gabriel R. and John, Volker and Knobloch, Petr},
title = {A local projection stabilization finite element method with nonlinear crosswind diffusion for convection-diffusion-reaction equations},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
volume = {47},
year = {2013},
pages = {1335-1366},
doi = {10.1051/m2an/2013071},
mrnumber = {3100766},
language = {en},
url = {http://dml.mathdoc.fr/item/M2AN_2013__47_5_1335_0}
}
Barrenechea, Gabriel R.; John, Volker; Knobloch, Petr. A local projection stabilization finite element method with nonlinear crosswind diffusion for convection-diffusion-reaction equations. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 47 (2013) pp. 1335-1366. doi : 10.1051/m2an/2013071. http://gdmltest.u-ga.fr/item/M2AN_2013__47_5_1335_0/
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