Abstract
A two-grid algorithm for discontinuous Galerkin approximations to nonlinear Sobolev equations is proposed. H1 norm error estimate of the two-grid method for the nonlinear parabolic problem is derived. The analysis shows that our two-grid discontinuous Galerkin algorithm will achieve asymptotically optimal approximation as long as the mesh sizes satisfy $h = O(H^{\frac {r+1}{r}})$ , where r is the order of the discontinuous finite element space. The numerical experiments are presented to prove the efficiency of our algorithm.
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