Nitsche’s method for unilateral contact problems
| Autor: | Rolf Stenberg, Tom Gustafsson, Juha Videman |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Nitsche's method
Unilateral contact General Mathematics ta111 Scalar (physics) Stabilised finite elements Estimator 010103 numerical & computational mathematics 01 natural sciences A posteriori estimate Finite element method Mathematics::Numerical Analysis symbols.namesake Lagrange multiplier 0103 physical sciences Variational inequality symbols Applied mathematics A priori and a posteriori 0101 mathematics Signorini problem 010303 astronomy & astrophysics Mathematics |
| Zdroj: | Portugaliae Mathematica. 75:189-204 |
| ISSN: | 0032-5155 |
| Popis: | We derive optimal a priori and a posteriori error estimates for Nitsche's method applied to unilateral contact problems. Our analysis is based on the interpretation of Nitsche's method as a stabilised finite element method for the mixed Lagrange multiplier formulation of the contact problem wherein the Lagrange multiplier has been eliminated elementwise. To simplify the presentation, we focus on the scalar Signorini problem and outline only the proofs of the main results since most of the auxiliary results can be traced to our previous works on the numerical approximation of variational inequalities. We end the paper by presenting results of our numerical computations which corroborate the efficiency and reliability of the a posteriori estimators. |
| Databáze: | OpenAIRE |
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