A Multigrid Semismooth Newton Method for Contact Problems in Linear Elasticity
نویسندگان
چکیده
A multigrid semismooth Newton method for elastic contact problems is developed and analyzed. We show that after a suitable regularization of the contact problem superlinear local convergence is obtained for a class of semismooth Newton methods. In addition, an estimate for the order of the error introduced by the regularization is derived. The main part of the paper is devoted to the analysis of a multilevel preconditioner for the semismooth Newton system. We prove a rigorous bound for the contraction rate of the multigrid cycle which is robust with respect to sufficiently small regularization parameters and the number of grid levels. Moreover, it applies to adaptively refined grids. The paper concludes with numerical results. Keywords
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