Evolving finite elements for advection diffusion with an evolving interface
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866918501246042112 |
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| author | Elliott, C. M. Ranner, T. Stepanov, P. |
| author_facet | Elliott, C. M. Ranner, T. Stepanov, P. |
| contents | The aim of this paper is to develop a numerical scheme to approximate evolving interface problems for parabolic equations based on the abstract evolving finite element framework proposed in (C M Elliott, T Ranner, IMA J Num Anal, 41:3, 2021, doi:10.1093/imanum/draa062). An appropriate weak formulation of the problem is derived for the use of evolving finite elements designed to accommodate a moving interface. Optimal order error bounds are proved for arbitrary order evolving isoparametric finite elements. The paper concludes with numerical results for a model problem verifying orders of convergence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_04850 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Evolving finite elements for advection diffusion with an evolving interface Elliott, C. M. Ranner, T. Stepanov, P. Numerical Analysis The aim of this paper is to develop a numerical scheme to approximate evolving interface problems for parabolic equations based on the abstract evolving finite element framework proposed in (C M Elliott, T Ranner, IMA J Num Anal, 41:3, 2021, doi:10.1093/imanum/draa062). An appropriate weak formulation of the problem is derived for the use of evolving finite elements designed to accommodate a moving interface. Optimal order error bounds are proved for arbitrary order evolving isoparametric finite elements. The paper concludes with numerical results for a model problem verifying orders of convergence. |
| title | Evolving finite elements for advection diffusion with an evolving interface |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2208.04850 |