Mixed finite element methods for two-body contact problems

Andreas Schroeder , Heiko Kleemann , Heribert Blum

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

MSC 2000

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

65N15 Error bounds

Abstract
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 $h$- and $p$-method. For this purpose, a discrete inf-sup condition is proven which, moreover, guarantees the stability of the mixed method. Numerical results confirm the theoretical findings.