A POSTERIORI ERROR ESTIMATES FOR HIGHER ORDER SPACE-TIME GALERKIN DISCRETIZATIONS OF NONLINEAR PARABOLIC PROBLEMS

Abstract

We deal with the numerical solution of nonlinear time-dependent convection-diffusionreaction equations with the aid of continuous and discontinuous Galerkin discretization of an arbitrary polynomial approximation degree. We derive a posteriori error estimates in the space-time mesh-dependent dual norm.

The estimates are based on the equilibrated flux reconstruction techniques which are locally computable. We prove the upper and lower bounds and present several numerical experiments justifying the theoretical results.

Keywords

• a posteriori error estimates
• equilibrated flux reconstruction
• nonlinear convection-diffusion
• reliability
• efficiency