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Stability estimates of the mortar finite element method for 3-dimensional problems. (English) Zbl 0922.65072
The main interest of the mortar finite element method is its ability to match different types of discretizations on adjacent subdomains even if they are from different types. In a previous paper, the authors have studied a multigrid algorithm for the mortar finite element method in 2D. This paper extends these results to 3D problems.
The statement of the problem and of its approximation is well detailed. Next, the convergence is carefully analyzed and includes LBB-condition, $$L_2$$-error estimate and condition number of the Schur complement in the smoother.
Unfortunately, no numerical experiments are included to attest the ability of this method.

##### 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 65F35 Numerical computation of matrix norms, conditioning, scaling 35J25 Boundary value problems for second-order elliptic equations 65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs 65F10 Iterative numerical methods for linear systems