A hybrid coupled finite-boundary element method in elasticity

Abstract We present a hybrid coupled finite-boundary element method for a mixed boundary-value problem in linear elasticity. 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. The Trefftz elements are then modelled with boundary potentials supported by the individual element boundaries, the so-called macro-elements. The coupling between the finite and macro-elements is accomplished by using a generalized compatibility condition in weak sense with mortar 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. By following Hsiao et al. [G.C. Hsiao, E. Schnack and W.L. Wendland, Hybrid coupled finite-boundary element methods for elliptic systems of second order, in preparation], we give the precise formulation of the method, its functional analytic setting as well as corresponding discretizations and asymptotic error estimates. For illustrations, some computational results are also included.

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