Two-grid discontinuous Galerkin method for convection–diffusion–reaction equations

Abstract

In this paper, we study a two-grid method based on discontinuous Galerkin discretization for the convection–diffusion–reaction equation. The two-grid algorithm consists two steps: first solving the original nonsymmetric problem on coarse grid, and then solving the corresponding positive definite diffusion problem on fine grid. Note that the number of degrees of freedom on coarse mesh is less than the ones on fine mesh. Moreover, the bilinear form of positive definite problem on fine mesh only depends on the diffusion coefficient. Therefore, the two-grid algorithm essentially transforms the DG solution of convection–diffusion–reaction equation into the approximation for the DG solution of diffusion equation. The corresponding error estimates of the two-grid solution are also provided. Numerical experiments are performed to verify the theoretical results.