On convergence of the penalty method for unilateral contact problems

Authors:
Franz Chouly;Patrick Hild
Affiliations:
Laboratoire de Mathématiques de Besançon, UMR CNRS 6623, Université de Franche Comté, 16 route de Gray, 25030 Besançon Cedex, France;Institut de Mathématiques de Toulouse, UMR 5219 (CNRS/INSAT/UT1/UT2/UT3), Université Paul Sabatier (UT3), 118 route de Narbonne, 31062 Toulouse Cedex 9, France
Venue:
Applied Numerical Mathematics
Year:
2013

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Abstract

We present a convergence analysis of the penalty method applied to unilateral contact problems in two and three space dimensions. We first consider, under various regularity assumptions on the exact solution to the unilateral contact problem, the convergence of the continuous penalty solution as the penalty parameter @e vanishes. Then, the analysis of the finite element discretized penalty method is carried out. Denoting by h the discretization parameter, we show that the error terms we consider give the same estimates as in the case of the constrained problem when the penalty parameter is such that @e=h. We finally extend the results to the case where given (Tresca) friction is taken into account.