Comparison of mixed $hp$-BEM (stabilized and non-stabilized) for frictional contact problems

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.