AN OPTIMAL UNIFORM A PRIORI ERROR ESTIMATE FOR AN UNSTEADY SINGULARLY PERTURBED PROBLEM

Abstract

A time dependent convection diffusion problem is discretized by the Galerkin finite element method in space with bilinear elements on a general layer adapted mesh and in time by discontinuous Galerkin method. We present optimal error estimates.

The estimates hold true for consistent stabilization too.

Keywords

• discontinuous Galerkin
• convection diffusion
• layer adapted mesh
• error estimate