On the adaptive coupling of FEM and BEM in 2–d–elasticity |
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| Authors: | C. Carstensen S.A. Funken E.P. Stephan |
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| Affiliation: | Mathematisches Seminar, Christian-Albrechts-Universit?t Kiel, Ludewig-Meyn-Strasse 4, D-24098 Kiel, Germany, DE
Institut für Angewandte Mathematik, UNI Hannover, Welfengarten 1, D-30167 Hannover, Germany, DE
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| Abstract: | 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 –version of the FEM/BEM–coupling. Illustrating numerical results are included. Received April 15, 1994 / Revised version received January 8, 1996 |
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| Keywords: | Mathematics Subject Classification (1991): 65N35 65R20 65D07 45L10 |
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