Error analysis of a two-grid discontinuous Galerkin method for non-linear parabolic equations

摘要

Discontinuous Galerkin (DG) approximations for non-linear parabolic problems are investigated. To linearize the discretized equations, we use a two-grid method involving a small non-linear system on a coarse gird of size H and a linear system on a fine grid of size h. Error estimates in H-1-norm are obtained, O(h(r) + Hr+1) where r is the order of the DG space. The analysis shows that our two-grid DG algorithm will achieve asymptotically optimal approximation as long as the mesh sizes satisfy h = O(H(r+1)/r). The numerical experiments verify the efficiency of our algorithm.