Postprocessing of a finite volume element method for semilinear parabolic problems

Yang, Min; Bi, Chunjia; Liu, Jiangguo

ESAIM: Modélisation mathématique et analyse numérique, Tome 43 (2009) no. 5, pp. 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.

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