## Analysis and convergence of a covolume method for the generalized Stokes problem

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**66**(1997), 85-104 Request permission

## 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 $L^2$ norm for the pressure and error in a mesh dependent $H^1$ norm as well as in the $L^2$ norm for the velocity are shown to be of first order, provided that the exact velocity is in $H^2$ and the true pressure in $H^1$. 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.## References

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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
- Received by editor(s): September 11, 1995
- Received by editor(s) in revised form: December 1, 1995
- © Copyright 1997 American Mathematical Society
- 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