Adaptive hp-FEM for the contact problem with Tresca friction in linear elasticity: The primal--dual formulation and a posteriori error estimation

Authors:
P. Dörsek;J. M. Melenk
Affiliations:
Vienna University of Technology, Wiedner Hauptstraße 8-10, A-1040 Vienna, Austria;Vienna University of Technology, Wiedner Hauptstraße 8-10, A-1040 Vienna, Austria
Venue:
Applied Numerical Mathematics
Year:
2010

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Abstract

We present an a priori analysis of the hp-version of the finite element method for the primal-dual formulation of frictional contact in linear elasticity. We employ a novel hp-mortar projection operator that is uniformly stable in the mesh width and grows slowly in the polynomial degree. We derive an hp-FEM residual error indicator, develop an hp-adaptive strategy that is based on testing for analyticity, and show in numerical examples that the adaptive algorithm can lead to exponential rates of convergence.