Postprocessing of a finite volume element method for semilinear parabolic problems

Min Yang; Chunjia Bi; Jiangguo Liu

ESAIM: Mathematical Modelling and Numerical Analysis (2009)

  • Volume: 43, Issue: 5, page 957-971
  • ISSN: 0764-583X

Abstract

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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 L2 and H1 norms for the standard finite volume element scheme and an improved error estimate in the H1 norm. Numerical results demonstrate the accuracy and efficiency of the procedure.

How to cite

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Yang, Min, Bi, Chunjia, and Liu, Jiangguo. "Postprocessing of a finite volume element method for semilinear parabolic problems." ESAIM: Mathematical Modelling and Numerical Analysis 43.5 (2009): 957-971. <http://eudml.org/doc/250638>.

@article{Yang2009,
abstract = { 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 L2 and H1 norms for the standard finite volume element scheme and an improved error estimate in the H1 norm. Numerical results demonstrate the accuracy and efficiency of the procedure. },
author = {Yang, Min, Bi, Chunjia, Liu, Jiangguo},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Error estimates; finite volume elements; postprocessing; semilinear parabolic problems; error estimates; finite volume element method; initial boundary value problem; numerical experiments},
language = {eng},
month = {6},
number = {5},
pages = {957-971},
publisher = {EDP Sciences},
title = {Postprocessing of a finite volume element method for semilinear parabolic problems},
url = {http://eudml.org/doc/250638},
volume = {43},
year = {2009},
}

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: Mathematical Modelling and Numerical Analysis
DA - 2009/6//
PB - EDP Sciences
VL - 43
IS - 5
SP - 957
EP - 971
AB - 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 L2 and H1 norms for the standard finite volume element scheme and an improved error estimate in the H1 norm. Numerical results demonstrate the accuracy and efficiency of the procedure.
LA - eng
KW - Error estimates; finite volume elements; postprocessing; semilinear parabolic problems; error estimates; finite volume element method; initial boundary value problem; numerical experiments
UR - http://eudml.org/doc/250638
ER -

References

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