Finite element methods for time-dependent convection–diffusion–reaction equations with small diffusion

Numerical studies of stabilized finite element methods for solving scalar time-dependent convection–diffusion–reaction equations with small diffusion are presented in this paper. These studies include the streamline-upwind Petrov–Galerkin (SUPG) method with different parameters, various spurious oscillations at layers diminishing (SOLD) methods, a local projection stabilization (LPS) scheme based on enrichment and two finite element method flux corrected transport (FEM-FCT) methods. The focus of the evaluation of the numerical results is on the reduction of spurious oscillations.