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Multiplier spaces for the mortar finite element method in three dimensions. (English) Zbl 1006.65129
The paper is concerned with mortar finite elements for second-order elliptic boundary value problems (modelled by the Poisson equation) on bounded polyhedral 3D-domains. After a brief introduction into the general method, abstract conditions on the multiplier space to be chosen are formulated which guarantee a stable and convergent mortar finite element method.
If the mesh is only locally (but not globally) quasi-uniform, an additional condition is needed which in general poses further restrictions on the triangulation. Three examples of multiplier spaces are presented which satisfy the abstract conditions: One is defined in terms of a dual basis, and the two others are based on finite volume approaches. Three numerical examples illustrate the method.
Reviewer: M.Plum (Karlsruhe)

MSC:
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65F10 Iterative numerical methods for linear systems
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
35J25 Boundary value problems for second-order elliptic equations
65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs
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