%0 Journal Article %1 gustafsson2020nitschetextquotesingles %A Gustafsson, Tom %A Stenberg, Rolf %A Videman, Juha %D 2020 %I Society for Industrial & Applied Mathematics (SIAM) %J SIAM Journal on Scientific Computing %K 65n30-pdes-bvps-finite-elements 74b05-classical-linear-elasticity 74m15-contact-mechanics-of-deformable-solids 74s05-finite-element-methods-for-solid-mechanics %N 2 %P B425--B446 %R 10.1137/19m1246869 %T On Nitsche's Method for Elastic Contact Problems %U https://epubs.siam.org/doi/10.1137/19M1246869 %V 42 %X We show quasi-optimality and a posteriori error estimates for the frictionless contact problem between two elastic bodies with a zero-gap function. The analysis is based on interpreting Nitsche's method as a stabilized finite element method for which the error estimates can be obtained with minimal regularity assumptions and without the saturation assumption. We present three different Nitsche's mortaring techniques for the contact boundary, each corresponding to a different stabilizing term. Our numerical experiments show the robustness of Nitsche's method and corroborate the efficiency of the a posteriori error estimators.

@article{gustafsson2020nitschetextquotesingles, abstract = { We show quasi-optimality and a posteriori error estimates for the frictionless contact problem between two elastic bodies with a zero-gap function. The analysis is based on interpreting Nitsche's method as a stabilized finite element method for which the error estimates can be obtained with minimal regularity assumptions and without the saturation assumption. We present three different Nitsche's mortaring techniques for the contact boundary, each corresponding to a different stabilizing term. Our numerical experiments show the robustness of Nitsche's method and corroborate the efficiency of the a posteriori error estimators.}, added-at = {2020-06-04T06:19:33.000+0200}, author = {Gustafsson, Tom and Stenberg, Rolf and Videman, Juha}, biburl = {https://www.bibsonomy.org/bibtex/280f9fe548acf55b1dfca34586a088df1/gdmcbain}, doi = {10.1137/19m1246869}, interhash = {ac037410cd69b84aa05c7a5fc3a2c7fd}, intrahash = {80f9fe548acf55b1dfca34586a088df1}, journal = {{SIAM} Journal on Scientific Computing}, keywords = {65n30-pdes-bvps-finite-elements 74b05-classical-linear-elasticity 74m15-contact-mechanics-of-deformable-solids 74s05-finite-element-methods-for-solid-mechanics}, month = jan, number = 2, pages = {B425--B446}, publisher = {Society for Industrial {\&} Applied Mathematics ({SIAM})}, timestamp = {2020-06-04T06:19:33.000+0200}, title = {On Nitsche's Method for Elastic Contact Problems}, url = {https://epubs.siam.org/doi/10.1137/19M1246869}, volume = 42, year = 2020 }