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

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

• nonlinear local projection stabilization
• solvability
• error estimates
• convection-diffusion-reaction equations