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

Andreas Schroeder

Preprint series: Institut für Mathematik, Humboldt-Universität zu Berlin (ISSN 0863-0976),

MSC 2000

65N30 Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods

Abstract
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.