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

Jiming Yang and Xiaoqing Xing

Applied Mathematics and Computation, 2019, vol. 346, issue C, 96-108

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.

Keywords: Two-grid; Nonlinear problems; Discontinuous Galerkin method; Convergence estimate (search for similar items in EconPapers)
Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:346:y:2019:i:c:p:96-108

DOI: 10.1016/j.amc.2018.09.067

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