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

Authors:
Chuanjun Chen;Min Yang;Chunjia Bi
Affiliations:
Department of Mathematics and Information Science, Yantai University, Yantai, 264005, PR China;Department of Mathematics and Information Science, Yantai University, Yantai, 264005, PR China;Department of Mathematics and Information Science, Yantai University, Yantai, 264005, PR China
Venue:
Journal of Computational and Applied Mathematics
Year:
2009

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Abstract

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|lnH|). As a result, solving such a large class of nonlinear parabolic equations will not be much more difficult than solving one single linearized equation.