Error analysis of a finite element scheme for parametric mean curvature flow based on the DeTurck trick
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866918514769526784 |
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| author | Deckelnick, Klaus Styles, Vanessa |
| author_facet | Deckelnick, Klaus Styles, Vanessa |
| contents | The paper is concerned with the error analysis of a numerical scheme for the approximation of parametric mean curvature flow. The scheme we study is based on a reparametrization using the DeTurck trick and was proposed by Elliott and Fritz in [15]. In the semidiscrete case, for a spatial discretization by finite elements of order $k \geq 2$ we prove an optimal $H^1$-error estimate for the position vector. We present numerical experiments that confirm this error bound and demonstrate that the scheme has good properties with respect to the distribution of mesh points as already observed in [15]. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_21445 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Error analysis of a finite element scheme for parametric mean curvature flow based on the DeTurck trick Deckelnick, Klaus Styles, Vanessa Numerical Analysis Analysis of PDEs 65M60, 65M15, 35K93 The paper is concerned with the error analysis of a numerical scheme for the approximation of parametric mean curvature flow. The scheme we study is based on a reparametrization using the DeTurck trick and was proposed by Elliott and Fritz in [15]. In the semidiscrete case, for a spatial discretization by finite elements of order $k \geq 2$ we prove an optimal $H^1$-error estimate for the position vector. We present numerical experiments that confirm this error bound and demonstrate that the scheme has good properties with respect to the distribution of mesh points as already observed in [15]. |
| title | Error analysis of a finite element scheme for parametric mean curvature flow based on the DeTurck trick |
| topic | Numerical Analysis Analysis of PDEs 65M60, 65M15, 35K93 |
| url | https://arxiv.org/abs/2605.21445 |