Analysis and Convergence of a Covolume Method for the Generalized Stokes Problem

Author:
S. H. Chou

Journal:
Math. Comp. **66** (1997), 85-104

MSC (1991):
Primary 65N15, 65N30, 76D07; Secondary 35B45, 35J50

DOI:
https://doi.org/10.1090/S0025-5718-97-00792-8

MathSciNet review:
1372003

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Abstract | References | Similar Articles | Additional Information

Abstract: We introduce a covolume or MAC-like method for approximating the generalized Stokes problem. Two grids are needed in the discretization; a triangular one for the continuity equation and a quadrilateral one for the momentum equation. The velocity is approximated using nonconforming piecewise linears and the pressure piecewise constants. Error in the norm for the pressure and error in a mesh dependent norm as well as in the norm for the velocity are shown to be of first order, provided that the exact velocity is in and the true pressure in . We also introduce the concept of a network model into the discretized linear system so that an efficient pressure-recovering technique can be used to simplify a great deal the computational work involved in the augmented Lagrangian method. Given is a very general decomposition condition under which this technique is applicable to other fluid problems that can be formulated as a saddle-point problem.

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Additional Information

**S. H. Chou**

Affiliation:
Department of Mathematics and Statistics, Bowling Green State University, Bowling Green, Ohio 43402-0221

Email:
chou@zeus.bgsu.edu

DOI:
https://doi.org/10.1090/S0025-5718-97-00792-8

Keywords:
Covolume methods,
augmented Lagrangian method,
nonconforming mixed finite element,
network models

Received by editor(s):
September 11, 1995

Received by editor(s) in revised form:
December 1, 1995

Article copyright:
© Copyright 1997
American Mathematical Society