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Domain decomposition and mixed finite element methods for elliptic problems. (English) Zbl 0661.65105
Domain decomposition methods for partial differential equations, 1st Int. Symp., Paris/France 1987, 144-172 (1988).
[For the entire collection see Zbl 0649.00019.]
The numerical solution of elliptic partial differential problems with nonconstant coefficients is described using the domain decomposition methods based on a mixed formulation and mixed finite element approximations. Two families of conjugate gradient algorithms taking advantage of domain decomposition are discussed and their performance are evaluated by means of some numerical experiments, some of them concerning practical situations arising from the modeling of the flow in porous media.
Reviewer: J.Vaníček

MSC:
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
76S05 Flows in porous media; filtration; seepage
35J25 Boundary value problems for second-order elliptic equations