Summary.
This paper concerns the combination of the finite element method (FEM) and the boundary element method (BEM) using the symmetric coupling. As a model problem in two dimensions we consider the Hencky material (a certain nonlinear elastic material) in a bounded domain with Navier–Lamé differential equation in the unbounded complementary domain. Using some boundary integral operators the problem is rewritten such that the Galerkin procedure leads to a FEM/BEM coupling and quasi–optimally convergent discrete solutions. Beside this a priori information we derive an a posteriori error estimate which allows (up to a constant factor) the error control in the energy norm. Since information about the singularities of the solution is not available a priori in many situation and having in mind the goal of an automatic mesh–refinement we state adaptive algorithms for the \(h\)–version of the FEM/BEM–coupling. Illustrating numerical results are included.
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Received April 15, 1994 / Revised version received January 8, 1996
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Carstensen, C., Funken, S. & Stephan, E. On the adaptive coupling of FEM and BEM in 2–d–elasticity. Numer. Math. 77, 187–221 (1997). https://doi.org/10.1007/s002110050283
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DOI: https://doi.org/10.1007/s002110050283