Abstract

In this talk we report on recent progress in the solution of various non-smooth free boundary value problems that arise in contact mechanics, including unilateral contact with Tresca friction and non-monotone adhesion/delamination problems. We analyse these problems and employ for their numerical treatment optimization and regularization techniques combined with fi nite element discretisation.

This presentation is based on the recent papers [1, 2] and the recent PhD Thesis [3] of N. Ovcharova.

[1] J.Gwinner, hp-FEM convergence for unilateral contact problems with Tresca friction in plane linear elastostatics, J. Comput. Appl. Math. 254 (2013) 175 -184 [2] N. Ovcharova and J.Gwinner, A study of regularization techniques of nondi erentiable optimization in view of application to hemivariational inequalities, J. Optim Theory Appl., DOI 10 .1007/s10957-014-0521-y (2014) [3] N. Ovcharova, Regularization Methods and Finite Element Approximation of Some Hemivariational Inequalities with Applications to Nonmonotone Contact Problems, Ph.D. Thesis, Universitaet der Bundeswehr Muenchen, 2012.