Stabilized Finite Element Methods with Shock-Capturing for Nonlinear Convection–Diffusion-Reaction Models

Abstract

In this work stabilized higher-order finite element approximations of convection-diffusion-reactionsmodels with nonlinear reactionmechanisms are stud- ied. Streamline upwind Petrov–Galerkin (SUPG) stabilization together with aniso- tropic shock-capturing as an additional stabilization in crosswind-direction is used. The parameter design of the scheme is described precisely and error estimates are provided. Theoretical results are illustrated by numerical computations. The work extends former investigations for linear problems to more realistic nonlinearmodels.