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Analysis of the Schwarz algorithm for mixed finite elements methods. (English) Zbl 0765.65104

The paper is concerned with second-order elliptic differential equations in divergence form, subject to Neumann boundary conditions. Since the authors are interested in accurate numerical calculation of the flux variable, the direct application of the standard Galerkin method is unsatisfactory. Therefore, a mixed finite element method is applied to a transformed problem for pressure and flux.
To avoid difficulties with the saddle point character of this problem, the pressure is eliminated through the use of substructures of the domain. The remaining elliptic problem for the flux is treated by the Schwarz alternating (domain decomposition) algorithm, and convergence results for the method are established.

MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
65F10 Iterative numerical methods for linear systems
35J25 Boundary value problems for second-order elliptic equations
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References:

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