Error estimates in , and

in covolume methods

for elliptic and parabolic problems:

A unified approach

Authors:
So-Hsiang Chou and Qian Li

Journal:
Math. Comp. **69** (2000), 103-120

MSC (1991):
Primary 65F10, 65N20, 65N30

DOI:
https://doi.org/10.1090/S0025-5718-99-01192-8

Published electronically:
August 25, 1999

MathSciNet review:
1680859

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we consider covolume or finite volume element methods for variable coefficient elliptic and parabolic problems on convex smooth domains in the plane. We introduce a general approach for connecting these methods with finite element method analysis. This unified approach is used to prove known convergence results in the norms and new results in the max-norm. For the elliptic problems we demonstrate that the error between the exact solution and the approximate solution in the maximum norm is in the linear element case. Furthermore, the maximum norm error in the gradient is shown to be of first order. Similar results hold for the parabolic problems.

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Additional Information

**So-Hsiang Chou**

Affiliation:
Department of Mathematics and Statistics, Bowling Green State University, Bowling Green, Ohio 43403-0221, U.S.A.

Email:
chou@zeus.bgsu.edu; http://www-math.bgsu.edu/~chou

**Qian Li**

Affiliation:
Department of Mathematics, Shandong Normal University, Shandong, China

DOI:
https://doi.org/10.1090/S0025-5718-99-01192-8

Keywords:
Covolume methods,
finite volume methods,
generalized difference methods,
network methods,
finite volume element

Received by editor(s):
March 19, 1996

Received by editor(s) in revised form:
April 22, 1996

Published electronically:
August 25, 1999

Article copyright:
© Copyright 1999
American Mathematical Society