Abstract: In this talk, mixed finite element methods are presented for contact problems which are described by Signorini's problem. The discretization is based on a mixed variational formulation and includes higher-order finite elements. To guarantee the unique existence of the solution of the mixed method, a discrete inf-sup condition is considered where approximation results for the p-method of finite elements and some inverse estimates for higher-order polynomials are applied. Furthermore, a posteriori error estimates and their application within hp-adaptive refinement strategies are presented. At last, the application of the error estimates to time-dependent problems is discussed.
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