Multiplier spaces for the mortar finite element method in three dimensions (Q2719220)

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.NEWLINENEWLINENEWLINEIf 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.