Postprocessing of a finite volume element method for semilinear parabolic problems
Department of Mathematics, Yantai University, Yantai, Shandong 264005, P. R. China. firstname.lastname@example.org; email@example.com
2 Department of Mathematics, Colorado State University, Fort Collins, CO 80523-1874, USA. firstname.lastname@example.org
Revised: 8 December 2008
In this paper, we study a postprocessing procedure for improving accuracy of the finite volume element approximations of semilinear parabolic problems. The procedure amounts to solve a source problem on a coarser grid and then solve a linear elliptic problem on a finer grid after the time evolution is finished. We derive error estimates in the L2 and H1 norms for the standard finite volume element scheme and an improved error estimate in the H1 norm. Numerical results demonstrate the accuracy and efficiency of the procedure.
Mathematics Subject Classification: 65N30 / 65N15
Key words: Error estimates / finite volume elements / postprocessing / semilinear parabolic problems
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