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: Mathematical Modelling and Numerical Analysis , Tome 43 (2009) no. 5, pp. 957-971.

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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 L 2 and H 1 norms for the standard finite volume element scheme and an improved error estimate in the H 1 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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     title = {Postprocessing of a finite volume element method for semilinear parabolic problems},
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Yang, Min; Bi, Chunjia; Liu, Jiangguo. Postprocessing of a finite volume element method for semilinear parabolic problems. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 43 (2009) no. 5, pp. 957-971. doi : 10.1051/m2an/2009017. https://geodesic-test.mathdoc.fr/articles/10.1051/m2an/2009017/

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