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 Liu<sup>2

1</sup>  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


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