Hybrid coupled finite-boundary element methods for elliptic systems of second order

In this hybrid method, we consider, in addition to traditional finite eleme nts, the Trefftz elements for which the governing equations of equilibrium are required to be satisfied a priori within the subdomain elements. If the Trefftz elements are modelled with boundary potentials supported by the in dividual element boundaries, this defines the so-called macro-elements. The se allow one to handle in particular situations involving singular features such as cracks, inclusions, corners and notches providing: a locally high resolution of the desired stress fields, in combination with a traditional global variational FEM analysis. The global stiffness matrix is here sparse as the one in conventional FEM. In addition, with slight modifications, th e macro-elements can be incorporated into standard commercial FEM codes. Th e coupling between the elements is modelled by using a generalized compatib ility condition in a weak sense with additional elements on the skeleton. T he latter allows us to relax the continuity requirements for the global sol ution field. In particular, the mesh points of the macro-elements can be ch osen independently of the nodes of the FEM structure. This approach permits the combination of independent meshes and also the exploitation of modern parallel computing facilities. We present here the formulation of the metho d and its functional analytic setting as well as corresponding discretizati ons and asymptotic error estimates. For illustration, we include some compu tational results in two- and three-dimensional elasticity. (C) 2000 Elsevie r Science S.A. All rights reserved. MSC. 73V10; 65N38; 65N30; 65N55; 65Y05.