Path-following and augmented Lagrangian methods for contact problems in linear elasticity. (English) Zbl 1119.49028

Summary: A certain regularization technique for contact problems leads to a family of problems that can be solved efficiently using infinite-dimensional semismooth Newton methods, or in this case equivalently, primal-dual active set strategies. We present two procedures that use a sequence of regularized problems to obtain the solution of the original contact problem: first-order augmented Lagrangian, and path-following methods. The first strategy is based on a multiplier-update, while path-following with respect to the regularization parameter uses theoretical results about the path-value function to increase the regularization parameter appropriately. Comprehensive numerical tests investigate the performance of the proposed strategies for both a 2D as well as a 3D contact problem.


49M15 Newton-type methods
74M15 Contact in solid mechanics
49M37 Numerical methods based on nonlinear programming
65K05 Numerical mathematical programming methods
49S05 Variational principles of physics


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