A GOAL-ORIENTED HIGH-ORDER ANISOTROPIC MESH ADAPTATION USING DISCONTINUOUS GALERKIN METHOD FOR LINEAR CONVECTION-DIFFUSION-REACTION PROBLEMS

Abstract

We deal with the numerical solution of a linear convection-diffusion-reaction equation using the discontinuous Galerkin method of arbitrary polynomial approximation degree on anisotropic triangular grids. We derive a posteriori goal-oriented error estimates taking into account the anisotropy of mesh elements.

The resulting error estimates are employed for the construction of an anisotropic mesh adaptation algorithm which locally optimizes the size and shape of mesh elements. The computational performance is demonstrated by several numerical experiments.

Keywords

• goal-oriented error estimates
• discontinuous Galerkin method
• anisotropic mesh adaptation