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

Maischak, Matthias; Stephan, Ernst P.

Appl. Numer. Math. 54, No. 3-4, 425-449 (2005).

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.

MSC:

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

Keywords:

Boundary elements; \(hp\)-version; Steklov-Poincaré operator; Signorini contact; Hierarchical error estimator

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