A priori error estimates for hp penalty BEM for contact problems in elasticity

The purpose of the paper is to obtain a priori error estimates for the hp-version of penalty Galerkin BEM applied to frictionless contact problems in elasticity. The error analysis is divided into two parts. At first we consider the error caused by the approximation of the variational inequality (or Lagrange multiplier) formulation with the penalty problem. Under additional regularity assumptions we derive a linear convergence rate with respect to the penalty parameter. Then the discretization error between the solution of the penalty problem and its Galerkin approximation is considered. We show two types of the best approximation property which is similar to the Cea’s lemma, but the estimate depends on the penalty parameter. Finally, we derive an a priori estimate for the error between the exact solution u of the variational inequality and the boundary element Galerkin solution of the penalty problem. For u ∈ H ∼ 3 / 2 ( Γ C ∪ Γ N ) we obtain the convergence rate O ( ( h / p ) 1 - ϵ ) when choosing the penalty parameter ε = C ∼ ( h / p ) 1 - ϵ for arbitrary fixed ϵ ∈ ( 0 ; 1 ) and C ∼ > 0 .