Postprocessing of a finite volume element method for semilinear parabolic problems
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 43 (2009) no. 5, p. 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 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 : https://doi.org/10.1051/m2an/2009017
Classification:  65N30,  65N15
Keywords: error estimates, finite volume elements, postprocessing, semilinear parabolic problems
@article{M2AN_2009__43_5_957_0,
     author = {Yang, Min and Bi, Chunjia and Liu, Jiangguo},
     title = {Postprocessing of a finite volume element method for semilinear parabolic problems},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {43},
     number = {5},
     year = {2009},
     pages = {957-971},
     doi = {10.1051/m2an/2009017},
     zbl = {1176.65102},
     mrnumber = {2559740},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_2009__43_5_957_0}
}
Yang, Min; Bi, Chunjia; Liu, Jiangguo. Postprocessing of a finite volume element method for semilinear parabolic problems. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 43 (2009) no. 5, pp. 957-971. doi : 10.1051/m2an/2009017. http://www.numdam.org/item/M2AN_2009__43_5_957_0/

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