Mixed FEM of higher-order for a frictional contact problem

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

65N15 Error bounds

Abstract
This paper presents mixed finite element methods of higher-order for an idealized frictional contact problem in linear elasticity. The approach relies on a saddle point formulation where the frictional contact condition is captured by a Lagrange multiplier. The convergence of the mixed scheme is proven and some a~priori estimates for the $h$- and $p$-method are derived. Furthermore, a~posteriori error estimates are presented which rely on the estimation of the discretization error of an auxiliary problem and some further terms capturing the error in the friction and complementary conditions. Numerical results confirm the applicability of the a~posteriori error estimates within $h$- and $hp$-adaptive schemes.