Geodesic
The method of successive approximations for solving quasi-variational Signorini inequality
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 1 (2017), pp. 44-52

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We consider the method of successive approximations for solving the semicoercive quasi-variational Signorini inequality corresponding to the contact problem of elasticity theory with friction. Each outer step of the iterative process involves the Signorini problem with given friction, which is solved by the Uzawa method based on an iterative proximal regularization of a modified Lagrangian functional. We investigate stabilization sequence of auxiliary finite element solutions on the outer steps of the method of successive approximations and present the results of numerical calculation.
Keywords: contact problem of the elasticity theory, Lagrangian functional, saddle point, Uzawa method, proximal regularization, finite element method. 
@article{IVM_2017_1_a4,
     author = {R. V. Namm and G. I. Tsoi},
     title = {The method of successive approximations for solving quasi-variational {Signorini} inequality},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {44--52},
     publisher = {mathdoc},
     number = {1},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2017_1_a4/}
}
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R. V. Namm; G. I. Tsoi. The method of successive approximations for solving quasi-variational Signorini inequality. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 1 (2017), pp. 44-52. http://geodesic.mathdoc.fr/item/IVM_2017_1_a4/