A High-Order Conservative Cut Finite Element Method for Problems in Time-Dependent Domains
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866917653771190272 |
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| author | Myrbäck, Sebastian Zahedi, Sara |
| author_facet | Myrbäck, Sebastian Zahedi, Sara |
| contents | A mass-conservative high-order unfitted finite element method for convection-diffusion equations in evolving domains is proposed. The space-time method presented in [P. Hansbo, M. G. Larson, S. Zahedi, Comput. Methods Appl. Mech. Engrg. 307 (2016)] is extended to naturally achieve mass conservation by utilizing Reynold's transport theorem. Furthermore, by partitioning the time-dependent domain into macroelements, a more efficient stabilization procedure for the cut finite element method in time-dependent domains is presented. Numerical experiments illustrate that the method fulfills mass conservation, attains high-order convergence, and the condition number of the resulting system matrix is controlled while sparsity is increased. Problems in bulk domains as well as coupled bulk-surface problems are considered. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_10756 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A High-Order Conservative Cut Finite Element Method for Problems in Time-Dependent Domains Myrbäck, Sebastian Zahedi, Sara Numerical Analysis 65N30, 65N22, 65N85, 65N99 A mass-conservative high-order unfitted finite element method for convection-diffusion equations in evolving domains is proposed. The space-time method presented in [P. Hansbo, M. G. Larson, S. Zahedi, Comput. Methods Appl. Mech. Engrg. 307 (2016)] is extended to naturally achieve mass conservation by utilizing Reynold's transport theorem. Furthermore, by partitioning the time-dependent domain into macroelements, a more efficient stabilization procedure for the cut finite element method in time-dependent domains is presented. Numerical experiments illustrate that the method fulfills mass conservation, attains high-order convergence, and the condition number of the resulting system matrix is controlled while sparsity is increased. Problems in bulk domains as well as coupled bulk-surface problems are considered. |
| title | A High-Order Conservative Cut Finite Element Method for Problems in Time-Dependent Domains |
| topic | Numerical Analysis 65N30, 65N22, 65N85, 65N99 |
| url | https://arxiv.org/abs/2404.10756 |