Two-grid methods for finite volume element approximations of nonlinear parabolic equations

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:228

Article

Chen, Chuanjun¹  Yang, Min¹  Bi, Chunjia¹ 

[1] Yantai Univ, Dept Math & Informat Sci, Yantai 264005, Peoples R China

关键词: Two-grid method;    Finite volume element method;    Error estimates;   

DOI  :  10.1016/j.cam.2008.09.001

来源: Elsevier

【 摘 要 】

Two-grid methods are studied for solving a two dimensional nonlinear parabolic equation using finite volume element method. The methods are based on one coarse-grid space and one fine-grid space. The nonsymmetric and nonlinear iterations are only executed on the coarse grid and the fine-grid solution can be obtained in a single symmetric and linear step. It is proved that the coarse grid can be much coarser than the fine grid. The two-grid methods achieve asymptotically optimal approximation as long as the mesh sizes satisfy h = O(H-3 vertical bar In H vertical bar). As a result, solving such a large class of nonlinear parabolic equations will not be much more difficult than solving one single linearized equation. (c) 2008 Elsevier B.V. All rights reserved.

【 授权许可】

Free