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Postprocessing of a finite volume element method for semilinear parabolic problems

Published online by Cambridge University Press:  12 June 2009

Min Yang ,
Chunjia Bi  and
Jiangguo Liu
Min Yang
Affiliation:
Department of Mathematics, Yantai University, Yantai, Shandong 264005, P. R. China. yang@ytu.edu.cn; bicj@ytu.edu.cn
Chunjia Bi
Affiliation:
Department of Mathematics, Yantai University, Yantai, Shandong 264005, P. R. China. yang@ytu.edu.cn; bicj@ytu.edu.cn
Jiangguo Liu
Affiliation:
Department of Mathematics, Colorado State University, Fort Collins, CO 80523-1874, USA. liu@math.colostate.edu
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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.

Keywords

Error estimatesfinite volume elementspostprocessingsemilinear parabolic problems
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 43 , Issue 5 , September 2009 , pp. 957 - 971
Copyright
© EDP Sciences, SMAI, 2009

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