Numerical analysis of a constrained strain energy minimization problem
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866918314925621248 |
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| author | Aleman, Tilman Reusken, Arnold |
| author_facet | Aleman, Tilman Reusken, Arnold |
| contents | We consider a setting in which an evolving surface is implicitly characterized as the zero level of a level set function. Such an implicit surface does not encode any information about the path of a single point on the evolving surface. In the literature different approaches for determining a velocity that induces corresponding paths of points on the surface have been proposed. One of these is based on minimization of the strain energy functional. This then leads to a constrained minimization problem, which has a corresponding equivalent formulation as a saddle point problem. The main topic of this paper is a detailed analysis of this saddle point problem and of a finite element discretization of this problem. We derive well-posedness results for the continuous and discrete problems and optimal error estimates for a finite element discretization that uses standard $H^1$-conforming finite element spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_19089 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Numerical analysis of a constrained strain energy minimization problem Aleman, Tilman Reusken, Arnold Numerical Analysis We consider a setting in which an evolving surface is implicitly characterized as the zero level of a level set function. Such an implicit surface does not encode any information about the path of a single point on the evolving surface. In the literature different approaches for determining a velocity that induces corresponding paths of points on the surface have been proposed. One of these is based on minimization of the strain energy functional. This then leads to a constrained minimization problem, which has a corresponding equivalent formulation as a saddle point problem. The main topic of this paper is a detailed analysis of this saddle point problem and of a finite element discretization of this problem. We derive well-posedness results for the continuous and discrete problems and optimal error estimates for a finite element discretization that uses standard $H^1$-conforming finite element spaces. |
| title | Numerical analysis of a constrained strain energy minimization problem |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2411.19089 |