A comparative study of finite element methods for a class of harmonic map heat flow problems
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914010984611840 |
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| author | Nguyen, Nam Anh Reusken, Arnold |
| author_facet | Nguyen, Nam Anh Reusken, Arnold |
| contents | In this paper, we review and systematically compare three finite element discretization methods for a harmonic map heat flow problem from the unit disk in $\mathbb{R}^2$ to the unit sphere in $\mathbb{R}^3$ in an unified framework. Numerical tests validate the convergence rates in a regime of smooth solutions and are used to compare the methods in terms of computational efficiency. For one of the methods a discrete inf-sup stability result is derived. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_20590 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A comparative study of finite element methods for a class of harmonic map heat flow problems Nguyen, Nam Anh Reusken, Arnold Numerical Analysis In this paper, we review and systematically compare three finite element discretization methods for a harmonic map heat flow problem from the unit disk in $\mathbb{R}^2$ to the unit sphere in $\mathbb{R}^3$ in an unified framework. Numerical tests validate the convergence rates in a regime of smooth solutions and are used to compare the methods in terms of computational efficiency. For one of the methods a discrete inf-sup stability result is derived. |
| title | A comparative study of finite element methods for a class of harmonic map heat flow problems |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2508.20590 |