*(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.

##### MSC:

65N30 | Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (BVP of PDE) |

65F10 | Iterative methods for linear systems |

65N12 | Stability and convergence of numerical methods (BVP of PDE) |

35J05 | Laplacian operator, reduced wave equation (Helmholtz equation), Poisson equation |

35J25 | Second order elliptic equations, boundary value problems |

65N50 | Mesh generation and refinement (BVP of PDE) |