Two-grid finite volume element methods for semilinear parabolic problems

Authors:
Chuanjun Chen;Wei Liu
Affiliations:
Department of Mathematics and Information Science, Yantai University, Yantai, 264005, PR China;School of Statistics and Mathematics, Shandong Economic University, Jinan, 250014, PR China
Venue:
Applied Numerical Mathematics
Year:
2010

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Abstract

Two-grid finite volume element methods, based on two linear conforming finite element spaces on one coarse grid and one fine grid, are presented and studied for two-dimensional semilinear parabolic problems. With the proposed techniques, solving the nonsymmetric and nonlinear system on the fine space is reduced to solving a symmetric and linear system on the fine space and solving the nonsymmetric and nonlinear system on a much smaller space. Convergence estimates are derived to justify the efficiency of the proposed two-grid algorithms. It is proved that the coarse grid can be much coarser than the fine grid. As a result, solving such a large class of semilinear parabolic problems will not be much more difficult than solving one single linearized equation. In the end a numerical example is presented to validate the usefulness and efficiency of the method.