Mixed finite element methods for two-body contact problems

This paper presents mixed finite element methods of higher-order for two-body contact problems of linear elasticity. The discretization is based on a mixed variational formulation proposed by Haslinger et al. which is extended to higher-order finite elements. The main focus is on the convergence of the scheme and on a priori estimates for the hh- and the pp-method. For this purpose, a discrete inf–sup condition is proven which guarantees the stability of the mixed method. Numerical results confirm the theoretical findings.