Analysis of stabilized higher-order finite element approximation of nonstationary and nonlinear convection–diffusion–reaction equations

In this work the numerical approximation of unsteady and nonlinear convection–diffusion–reaction models with small diffusion by higher order finite element methods is studied. Streamline upwind Petrov–Galerkin (SUPG) stabilization together with anisotropic shock capturing as an additional stabilization in crosswind direction are used. Error analyses and the parameter design given in the literature are generalized to the case of nonlinear reaction rates. By numerical studies it is illustrated that the combination of these approximation techniques reduce spurious oscillations in crosswind direction and improve the accuracy of simulations.