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Zbl 0854.65091
Chou, S.H.
Analysis and convergence of a covolume method for the generalized Stokes problem. (English)
[J] Math. Comput. 66, No.217, 85-104 (1997). ISSN 0025-5718; ISSN 1088-6842/e

Summary: 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.

MSC 2000:: *65N15 Error bounds (BVP of PDE)
65N30 Finite numerical methods (BVP of PDE)
76D07 Stokes flows
35B45 A priori estimates
35J50 Systems of elliptic equations, variational methods

Keywords: covolume methods; augmented Lagrangian method; nonconforming mixed finite element; network models

Cited in: Zbl 1080.76038 Zbl 0947.65120

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