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A multigrid method for saddle point problems arising from mortar finite element discretizations. (English) Zbl 0958.65135
The author analyzes a multigrid algorithm for saddle point problems arising from mortar finite element discretizatoins. It is not required that the constraints at the interface are satisfied in each smooth step but the squared system is used. Using mesh dependent norms for the Lagrange multipliers, suitable approximation and smoothing properties are established. A convergence rate independent of the meshsize is obtained for the \(W\)-cycle.

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
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations
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