A nonlinear local projection stabilization for convection-diffusion-reaction equations

• ID: 2569, RIV: 10132931
• ISSN: not specified, ISBN: 978-3-642-33133-6
• source: Numerical Mathematics and Advanced Applications 2011
• keywords: nonlinear local projection stabilization; solvability; error estimates; convection-diffusion-reaction equations
• authors: Gabriel R. Barrenechea, Volker John, Petr Knobloch
• authors from KNM: Knobloch Petr

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.