A two-grid discontinuous Galerkin method for a kind of nonlinear parabolic problems

A discontinuous Galerkin approximation for the space variables with the backward Euler time discretisation for a kind of parabolic problems with the nonlinear diffusion, convection and source terms is investigated. To solve the strongly nonlinear algebra system, a two-grid method is proposed. With this algorithm, solving a nonlinear system on the fine discontinuous finite element space is reduced into solving a nonlinear problem on a coarse gird of size and solving a linear problem on a fine grid of size. Convergence estimates in H-1-norm are obtained. The numerical experiments are provided to confirm our theoretical analysis. (C) 2018 Elsevier Inc. All rights reserved.