An a posteriori error analysis based on equilibrated stresses for finite element approximations of frictional contact
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866910287975677952 |
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| author | Fontana, Ilaria Di Pietro, Daniele A. |
| author_facet | Fontana, Ilaria Di Pietro, Daniele A. |
| contents | We consider the unilateral contact problem between an elastic body and a rigid foundation in a description that includes both Tresca and Coulomb friction conditions. For this problem, we present an a posteriori error analysis based on an equilibrated stress reconstruction in the Arnold--Falk--Winther space that includes a guaranteed upper bound distinguishing the different components of the error. This analysis is the starting point for the development of an adaptive algorithm including a stopping criterion for the generalized Newton method. This algorithm is then used to perform numerical simulations that validate the theoretical results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_02944 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An a posteriori error analysis based on equilibrated stresses for finite element approximations of frictional contact Fontana, Ilaria Di Pietro, Daniele A. Numerical Analysis 74M15, 74S05, 65N15, 65N30, 65N50 We consider the unilateral contact problem between an elastic body and a rigid foundation in a description that includes both Tresca and Coulomb friction conditions. For this problem, we present an a posteriori error analysis based on an equilibrated stress reconstruction in the Arnold--Falk--Winther space that includes a guaranteed upper bound distinguishing the different components of the error. This analysis is the starting point for the development of an adaptive algorithm including a stopping criterion for the generalized Newton method. This algorithm is then used to perform numerical simulations that validate the theoretical results. |
| title | An a posteriori error analysis based on equilibrated stresses for finite element approximations of frictional contact |
| topic | Numerical Analysis 74M15, 74S05, 65N15, 65N30, 65N50 |
| url | https://arxiv.org/abs/2401.02944 |