Mixed Finite Element Methods of Higher-Order for Model Contact Problems

This paper presents mixed finite element methods of higher-order for a simplified Signorini problem and an idealized frictional problem. The discretization is based on a mixed variational formulation proposed by Haslinger et al. which is extended to higher-order finite elements. To guarantee the unique existence of the solution of the mixed method, a discrete inf-sup condition is proven. Approximation results of the p-method of finite elements and some inverse estimates for higher-order polynomials are applied. Numerical results confirm the theoretical findings.