Numerical analysis of a constrained strain energy minimization problem
| Autor: | Aleman, Tilman, Reusken, Arnold |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 24 pages, 9 figures |
| Databáze: | arXiv |
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