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Domain decomposition with nonmatching grids: Augmented Lagrangian approach. (English) Zbl 0849.65087
The authors consider the numerical solution of a second-order linear elliptic problem by a nonoverlapping decomposition technique. The constraint of displacement continuity at the interfaces is treated by a Lagrange multiplier method. The solution of this augmented Lagrangian formulation of the problem is constructed by a standard saddle-point algorithm. Finite element methods with matching and nonmatching grids are studied. The discrete algorithm converges linearly independent of the discretization step. A new preconditioner using fictitious overlapping and well adapted to three-dimensional elasticity problems is considered. The methods are tested by several numerical examples.

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
65F10 Iterative numerical methods for linear systems
65F35 Numerical computation of matrix norms, conditioning, scaling
35J25 Boundary value problems for second-order elliptic equations
74B20 Nonlinear elasticity
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