Postprocessing of a finite volume element method for semilinear parabolic problems

Yang, Min; Bi, Chunjia; Liu, Jiangguo

doi:10.1051/m2an/2009017

Yang, Min ; Bi, Chunjia ; Liu, Jiangguo ¹

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.

Résumé

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.

MR Zbl

DOI : 10.1051/m2an/2009017

Classification : 65N30, 65N15
Mots clés : error estimates, finite volume elements, postprocessing, semilinear parabolic problems

Affiliations des auteurs :

Yang, Min ; Bi, Chunjia ; Liu, Jiangguo ¹

¹ Department of Mathematics, Colorado State University, Fort Collins, CO 80523-1874, USA.

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     author = {Yang, Min and Bi, Chunjia and Liu, Jiangguo},
     title = {Postprocessing of a finite volume element method for semilinear parabolic problems},
     journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
     pages = {957--971},
     publisher = {EDP-Sciences},
     volume = {43},
     number = {5},
     year = {2009},
     doi = {10.1051/m2an/2009017},
     mrnumber = {2559740},
     zbl = {1176.65102},
     language = {en},
     url = {http://www.numdam.org/articles/10.1051/m2an/2009017/}
}

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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. http://www.numdam.org/articles/10.1051/m2an/2009017/

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