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arXiv · 1310.6325

Adaptive FE-BE coupling for strongly nonlinear transmission problems with friction II

Heiko Gimperlein·Ernst P. Stephan
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Abstract

This article discusses the well-posedness and error analysis of the coupling of finite and boundary elements for transmission or contact problems in nonlinear elasticity. It concerns W^{1,p}-monotone Hencky materials with an unbounded stress-strain relation, as they arise in the modelling of ice sheets, non-Newtonian fluids or porous media. For 1<p<2 the bilinear form of the boundary element method fails to be continuous in natural function spaces associated to the nonlinear operator. We propose a functional analytic framework for the numerical analysis and obtain a priori and a posteriori error estimates for Galerkin approximations to the resulting boundary/domain variational inequality. The a posteriori estimate complements recent estimates obtained for mixed finite element formulations of friction problems in linear elasticity.

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Heiko Gimperlein, Ernst P. Stephan. 2013-10-23. Adaptive FE-BE coupling for strongly nonlinear transmission problems with friction II. https://doi.org/10.1515/cmam-2022-0120

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