A PRIORI DIFFUSION-UNIFORM ERROR ESTIMATES FOR NONLINEAR SINGULARLY PERTURBED PROBLEMS: BDF2, MIDPOINT AND TIME DG

Abstract

This work deals with a nonlinear nonstationary semilinear singularly perturbed convectiondiffusion problem. We discretize this problem by the discontinuous Galerkin method in space and by the midpoint rule, BDF2 and quadrature variant of discontinuous Galerkin in time.

We present a priori error estimates for these three schemes that are uniform with respect to the diffusion coefficient going to zero and valid even in the purely convective case.

Keywords

• Discontinuous Galerkin method
• a priori error estimates
• nonlinear convection-diffusion equation
• diffusion-uniform error estimates