an:00963286
Zbl 0854.65091
Chou, S. H.
Analysis and convergence of a covolume method for the generalized Stokes problem
EN
Math. Comput. 66, No. 217, 85-104 (1997).
00038355
1997
j
65N15 65N30 76D07 35B45 35J50
covolume methods; augmented Lagrangian method; nonconforming mixed finite element; network models
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.