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A three-field domain decomposition method. (English) Zbl 0801.65116
Quarteroni, Alfio (ed.) et al., Domain decomposition methods in science and engineering. The sixth international conference on domain decomposition, Como, Italy, June 15-19, 1992. Providence, RI: American Mathematical Society. Contemp. Math. 157, 27-34 (1994).
The authors present a three-field formulation for second order linear elliptic problems which is well suited for non-overlapping domain decomposition methods. This new formulation of the continuous problem allows to use different discretization methods from one subdomain to another.
Furthermore, the authors propose a preconditioner for the Schur complement $$S_ h$$, where $$S_ h$$ is non-symmetric. Numerical examples show that the number of iterations of the preconditioned conjugate gradient method applied to the Schur complement system is independent of the meshsize parameter but depends on the number of subdomains.
For the entire collection see [Zbl 0785.00036].
Reviewer: M.Jung (Chemnitz)

##### MSC:
 65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 65N06 Finite difference methods for boundary value problems involving PDEs 65F10 Iterative numerical methods for linear systems 65F35 Numerical computation of matrix norms, conditioning, scaling 35J25 Boundary value problems for second-order elliptic equations