Article ID Journal Published Year Pages File Type
4641288 Journal of Computational and Applied Mathematics 2010 10 Pages PDF
Abstract

The two-grid method is studied for solving a two-dimensional second-order nonlinear hyperbolic equation using finite volume element method. The method is based on two different finite element spaces defined on one coarse grid with grid size HH and one fine grid with grid size hh, respectively. 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. A prior error estimate in the H1H1-norm is proved to be O(h+H3|lnH|)O(h+H3|lnH|) for the two-grid semidiscrete finite volume element method. With these proposed techniques, solving such a large class of second-order nonlinear hyperbolic equations will not be much more difficult than solving one single linearized equation. Finally, a numerical example is presented to validate the usefulness and efficiency of the method.

Related Topics
Physical Sciences and Engineering Mathematics Applied Mathematics
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