Adaptive \(hp\)-versions of BEM for Signorini problems. (English) Zbl 1114.74062

Summary: We analyze the \(hp\)-discretization of a boundary integral formulation for the Signorini contact problem of the Laplacian. We prove convergence of the bem Galerkin solution in the energy norm and obtain, under mild regularity assumptions, an a priori error estimate. Using a hierarchical subspace decomposition we derive a reliable and efficient a posteriori error estimate. Based on the hierarchical estimators we present a three-step \(hp\)-adaptive algorithm and present numerical results which yield appropriate mesh refinements and polynomial degree distributions.


74S15 Boundary element methods applied to problems in solid mechanics
65N38 Boundary element methods for boundary value problems involving PDEs
74M15 Contact in solid mechanics
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