%0 Generic %1 Burman2016Penalty %A Burman, Erik %A Hansbo, Peter %A Larson, Mats G. %D 2016 %J arXiv.org > Mathematics > Numerical Analysis %K 65n30-pdes-bvps-finite-elements 74m15-contact-mechanics-of-deformable-solids %N 3745 %T The Penalty Free Nitsche Method and Nonconforming Finite Elements for the Signorini Problem %U http://arxiv.org/abs/1609.03745 %V 1609 %X We design and analyse a Nitsche method for contact problems. Compared to the seminal work of Chouly and Hild (A Nitsche-based method for unilateral contact problems: numerical analysis. SIAM J. Numer. Anal. 51 (2013), no. 2) our method is constructed by expressing the contact conditions in a nonlinear function for the displacement variable instead of the lateral forces. The contact condition is then imposed using the nonsymmetric variant of Nitsche's method that does not require a penalty term for stability. Nonconforming piecewise affine elements are considered for the bulk discretization. We prove optimal error estimates in the energy norm.

@electronic{Burman2016Penalty, abstract = {{We design and analyse a Nitsche method for contact problems. Compared to the seminal work of Chouly and Hild (A Nitsche-based method for unilateral contact problems: numerical analysis. SIAM J. Numer. Anal. 51 (2013), no. 2) our method is constructed by expressing the contact conditions in a nonlinear function for the displacement variable instead of the lateral forces. The contact condition is then imposed using the nonsymmetric variant of Nitsche's method that does not require a penalty term for stability. Nonconforming piecewise affine elements are considered for the bulk discretization. We prove optimal error estimates in the energy norm.}}, added-at = {2019-03-01T00:11:50.000+0100}, archiveprefix = {arXiv}, author = {Burman, Erik and Hansbo, Peter and Larson, Mats G.}, biburl = {https://www.bibsonomy.org/bibtex/20694ca16f36b6a190a9c22c740cfc9c6/gdmcbain}, citeulike-article-id = {14687660}, citeulike-attachment-1 = {burman_16_penalty_1152819.pdf; /pdf/user/gdmcbain/article/14687660/1152819/burman_16_penalty_1152819.pdf; 23ff0274bbbe70c65aa248ea58476bcf22688b23}, citeulike-linkout-0 = {http://arxiv.org/abs/1609.03745}, citeulike-linkout-1 = {http://arxiv.org/pdf/1609.03745}, comment = {circulated by Tom Gustafsson 2019-02-10 for notation of angle brackets 'for boundary integration whenever it is useful to distinguish interior and boundary integrals'}, day = 13, eprint = {1609.03745}, file = {burman_16_penalty_1152819.pdf}, interhash = {ed3f4a6e0d89883d0a5a9f574864312d}, intrahash = {0694ca16f36b6a190a9c22c740cfc9c6}, journal = {arXiv.org > Mathematics > Numerical Analysis}, keywords = {65n30-pdes-bvps-finite-elements 74m15-contact-mechanics-of-deformable-solids}, month = sep, number = 3745, posted-at = {2019-02-10 22:31:32}, priority = {2}, timestamp = {2019-03-01T00:11:50.000+0100}, title = {The Penalty Free {N}itsche Method and Nonconforming Finite Elements for the {S}ignorini Problem}, url = {http://arxiv.org/abs/1609.03745}, volume = 1609, year = 2016 }