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.
| Original language | English |
|---|---|
| Pages (from-to) | B425-B446 |
| Number of pages | 22 |
| Journal | SIAM Journal on Scientific Computing |
| Volume | 42 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - 2020 |
| MoE publication type | A1 Journal article-refereed |
Funding
\ast Submitted to the journal's Computational Methods in Science and Engineering section February 25, 2019; accepted for publication (in revised form) January 6, 2020; published electronically March 23, 2020. https://doi.org/10.1137/19M1246869 \bfF \bfu \bfn \bfd \bfi \bfn \bfg : This work was supported by the Portuguese government through FCT (Fundacao para a Ciencia e a Tecnologia), I.P., under the projects PTDC/MAT-PUR/28686/2017 and UTAP-EXPL/MAT/0017/2017. \dagger Department of Mathematics and Systems Analysis, Aalto University, 00076 Aalto, Finland ([email protected], [email protected]). \ddagger CAMGSD/Departamento de Matem\a'tica, Universidade de Lisboa, Universidade de Lisboa, 1049-001 Lisbon, Portugal ([email protected]).
Keywords
- Elastic contact
- Nitsche's method
- Variational inequality
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