hp-BEM for frictional contact problems in linear elasticity

Abstract: 

A mixed formulation for a Tresca frictional contact problem in linear elasticity is considered in the context of boundary integral equations, which is later extended to Coulomb friction. The discrete Lagrange multiplier, an approximation of the surface traction on the contact boundary part, is a linear combination of biorthogonal basis functions. The biorthogonality allows to rewrite the variational inequality constraints as a simple set of complementary problems, thus enabling an efficient application of a semi-smooth Newton solver for the discrete mixed problems. Typically, the solution of frictional contact problems is of reduced regularity at the interface between contact to non-contact and from stick to slip. To identify the a priori unknown locations of these interfaces, a posteriori error estimations of residual and hierarchical type are introduced. For a stabilized version of our mixed formulation (with the Poincare-Steklov operator) we present also a priori estimates for the solution. Numerical results show the applicability of the error estimators and the superiority of hp-adaptivity compared to low order uniform and adaptive approaches.