Comparison of mixed -BEM (stabilized and non-stabilized) for frictional contact problems.pdfVIP

Journal of Computational and Applied Mathematics 295 (2016) 92–102 Contents lists available at ScienceDirect Journal of Computational and Applied Mathematics journal homepage: /locate/cam Comparison of mixed hp-BEM (stabilized and non-stabilized) for frictional contact problems Lothar Banz a, Ernst P. Stephan b,? a Department of Mathematics, University of Salzburg, Hellbrunner Stra?e 34, 5020 Salzburg, Austria b Institute of Applied Mathematics, Leibniz University Hannover, Welfengarten 1, 30167 Hannover, Germany article info Article history: Received 17 October 2014 Received in revised form 23 January 2015 Keywords: Frictional contact problems hp-adaptive BEM Stabilized and non-stabilized mixed BEM abstract We present boundary integral equation procedures for contact problems (with Tresca or Coulomb friction) which are based on mixed formulations where besides the displacement also the traction on the contact boundary part appears (as a Lagrange multiplier). This approach allows for an easy and efficient way to perform an hp-BE method by the use of biorthogonal basis functions. This is especially suited for applying the semi-smooth Newton (SSN) method which is a very efficient solver superior to standard algorithm like Uzawa. With an adaptive algorithm we perform locally mesh refinements and increase of polynomial degrees for the BE solution—thus correctly representing the contact phenomena. We also present as stabilized version of our mixed hp-BEM scheme with Gauss–Lobatto– Lagrange basis which circumvents the discrete inf–sup condition. Numerical results supporting our theory are reported. ? 2015 Elsevier B.V. All rights reserved. 1. Introduction Many physical applications like simulation of tire performances can be modeled by frictional contact problems [1,2], where often multi-body contact problems are reduced to a sequence of one-body contact problem by employing a Contactto-Neumann algorithm as in [3]. In the literature a huge number of discretization schemes