Optimal error estimates for nonstationary singularly perturbed problems for low discretization orders

Abstract

Nonstationary 1D singularly perturbed convection-diffusion equation is discretized in space by the finite element method on a Shishkin mesh and by time discontinuous Galerkin method. The resulting scheme is analyzed and diffusion-uniform error estimates are derived.

The key results are restricted to lower order space and time discretizations only.

Keywords

• singularly perturbed problems
• convection-diffusion
• discontinuous Galerkin method