Postprocessing of a finite volume element method for semilinear parabolic problems
Yang, Min ; Bi, Chunjia ; Liu, Jiangguo1
1 Department of Mathematics, Colorado State University, Fort Collins, CO 80523-1874, USA.
ESAIM: Modélisation mathématique et analyse numérique, Tome 43 (2009) no. 5, pp. 957-971.

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.

DOI : 10.1051/m2an/2009017
Classification : 65N30, 65N15
Mots-clés : error estimates, finite volume elements, postprocessing, semilinear parabolic problems
Yang, Min  ; Bi, Chunjia  ; Liu, Jiangguo 1

1 Department of Mathematics, Colorado State University, Fort Collins, CO 80523-1874, USA. 
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Yang, Min; Bi, Chunjia; Liu, Jiangguo. Postprocessing of a finite volume element method for semilinear parabolic problems. ESAIM: Modélisation mathématique et analyse numérique, Tome 43 (2009) no. 5, pp. 957-971. doi : 10.1051/m2an/2009017. https://www.numdam.org/articles/10.1051/m2an/2009017/

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