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Postprocessing of a finite volume element methodfor 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 improvingaccuracy of the finite volume element approximations of semilinearparabolic problems. The procedure amounts to solve a source problemon a coarser grid and then solve a linear elliptic problem on afiner grid after the time evolution is finished. We derive errorestimates in the L 2 and H 1 norms for the standard finitevolume element scheme and an improved error estimate in the H 1 norm. Numerical results demonstrate the accuracy and efficiency ofthe 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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