Stabilized mixed hp-BEM for frictional contact problems in linear elasticity

Lothar Banz, Heiko Gimperlein, Abderrahman Issaoui, Ernst P Stephan

Research output: Contribution to journalArticle

7 Citations (Scopus)
49 Downloads (Pure)

Abstract

We analyze stabilized mixed hp-boundary element methods for frictional contact problems for the Lame equation. The stabilization technique circumvents the discrete inf-sup condition for the mixed problem and thus allows us to use the same mesh and polynomial degree for the primal and dual variables. We prove a priori convergence rates in the case of Tresca friction, using Gauss-Legendre-Lagrange polynomials as test and trial functions for the Lagrange multiplier. Additionally, a residual based a posteriori error estimate for a more general class of discretizations is derived. It in particular applies to discretizations based on Bernstein polynomials for the discrete Lagrange multiplier, which we also analyze. The discretization and the a posteriori error estimate are extended to the case of Coulomb friction. Several numerical experiments underline our theoretical results, demonstrate the behavior of the method and its insensitivity to the scaling and perturbations of the stabilization term.
Original languageEnglish
Pages (from-to)217-263
Number of pages47
JournalNumerische Mathematik
Volume135
Issue number1
Early online date19 Mar 2016
DOIs
Publication statusPublished - Jan 2017

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