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Mixed FEM of higher‐order for a frictional contact problem
Author(s) -
Schröder Andreas
Publication year - 2011
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201110003
Subject(s) - a priori and a posteriori , lagrange multiplier , finite element method , discretization , saddle point , mathematics , unilateral contact , convergence (economics) , saddle , mathematical optimization , elasticity (physics) , error analysis , mathematical analysis , engineering , structural engineering , geometry , materials science , philosophy , epistemology , economics , composite material , economic growth
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. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)