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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.

Postprocessing of a finite volume element method for semilinear parabolic problems