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Issue ESAIM: M2AN
Volume 43, Number 5, September-October 2009
Page(s) 957 - 971
DOI 10.1051/m2an/2009017
Published online 12 June 2009

ESAIM: M2AN 43 (2009) 957-971
DOI: 10.1051/m2an/2009017

Postprocessing of a finite volume element method for semilinear parabolic problems

Min Yang1, Chunjia Bi1 and Jiangguo Liu2

1  Department of Mathematics, Yantai University, Yantai, Shandong 264005, P. R. China. yang@ytu.edu.cn; bicj@ytu.edu.cn
2  Department of Mathematics, Colorado State University, Fort Collins, CO 80523-1874, USA. liu@math.colostate.edu

Received April 25, 2008. Revised December 8, 2008. Published online June 12, 2009.

Abstract
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


© EDP Sciences, SMAI 2009


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