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 and norms for the standard finite volume element scheme and an improved error estimate in the norm. Numerical results demonstrate the accuracy and efficiency of the procedure.
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: 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://archive.numdam.org/articles/10.1051/m2an/2009017/} }
TY - JOUR AU - Yang, Min AU - Bi, Chunjia AU - Liu, Jiangguo TI - Postprocessing of a finite volume element method for semilinear parabolic problems JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2009 SP - 957 EP - 971 VL - 43 IS - 5 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/m2an/2009017/ DO - 10.1051/m2an/2009017 LA - en ID - M2AN_2009__43_5_957_0 ER -
%0 Journal Article %A Yang, Min %A Bi, Chunjia %A Liu, Jiangguo %T Postprocessing of a finite volume element method for semilinear parabolic problems %J ESAIM: Modélisation mathématique et analyse numérique %D 2009 %P 957-971 %V 43 %N 5 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/m2an/2009017/ %R 10.1051/m2an/2009017 %G en %F M2AN_2009__43_5_957_0
Yang, Min; Bi, Chunjia; Liu, Jiangguo. Postprocessing of a finite volume element method for semilinear parabolic problems. ESAIM: Modélisation mathématique et analyse numérique, Volume 43 (2009) no. 5, pp. 957-971. doi : 10.1051/m2an/2009017. http://archive.numdam.org/articles/10.1051/m2an/2009017/
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