Hybrid Coupled Finite-Boundary Element Methods for Elliptical Systems of Second Order
Date
2000
Journal Title
Journal ISSN
Volume Title
Publisher
Department of Mathematical Sciences
Abstract
In this hybrid method, we consider, in addition to traditional finite elements,
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 individual element boundaries, this defines
the so–called macro–elements. These allow one to handle in particular situations involv-ing
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 varia-tional
FEM analysis. The global stiffness matrix is here sparse as the one in conventional
FEM. In addition, with slight modifications, the macro–elements can be incorporated
into standard commercial FEM codes. The coupling between the elements is modelled
by using a generalized compatibility condition in a weak sense with additional elements
on the skeleton. The latter allows us to relax the continuity requirements for the global
displacement field. In particular, the mesh points of the macro–elements can be chosen
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 method and its functional analytic setting as well as
corresponding discretizations and asymptotic error estimates. For illustration, we include
some computational results in two– and three–dimensional elasticity.