Journal
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
Volume 228, Issue 1, Pages 123-132Publisher
ELSEVIER
DOI: 10.1016/j.cam.2008.09.001
Keywords
Two-grid method; Finite volume element method; Error estimates
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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.
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