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

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.

20 pages, corrected typos and improved exposition

References in corpus (4)

• Space-time adaptive finite elements for nonlocal parabolic variational inequalities
• Stabilized mixed hp-BEM for frictional contact problems in linear elasticity
• Adaptive FE-BE Coupling for Strongly Nonlinear Transmission Problems with Coulomb Friction
• Stability of symmetric and nonsymmetric FEM-BEM couplings for nonlinear elasticity problems