On finite element methods for 3D time–dependent convection–diffusion–reaction equations with small diffusion

Abstract

The paper studies finite element methods for the simulation of time–dependent convection–diffusion–reaction equations with small diffusion: the SUPG method, a SOLD method and two types of FEM–FCT methods. The methods are assessed, in particular with respect to the size of the spurious oscillations in the computed solutions, at a 3D example with nonhomogeneous Dirichlet boundary conditions and homogeneous Neumann boundary conditions.