Abstract
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 H1-norm are obtained. The numerical experiments are provided to confirm our theoretical analysis.
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