Binz, Tim ; Kovács, Balázs
Alternative Links zum Volltext:DOIVerlag
| Dokumentenart: | Artikel |
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| Titel eines Journals oder einer Zeitschrift: | Interfaces and Free Boundaries, Mathematical Analysis, Computation and Applications |
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| Verlag: | EUROPEAN MATHEMATICAL SOC-EMS |
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| Ort der Veröffentlichung: | BERLIN |
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| Band: | 25 |
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| Nummer des Zeitschriftenheftes oder des Kapitels: | 3 |
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| Seitenbereich: | S. 373-400 |
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| Datum: | 2023 |
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| Institutionen: | Mathematik |
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| Identifikationsnummer: | | Wert | Typ |
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| 10.4171/IFB/493 | DOI |
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| Stichwörter / Keywords: | CURVE SHORTENING FLOW; DIFFERENTIAL-EQUATIONS; GRADIENT FLOWS; SURFACES; APPROXIMATION; DIFFUSION; DRIVEN; SCHEME; . Mean curvature flow; higher codimension; evolving surface finite elements; backward difference formulas; error estimates |
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| Dewey-Dezimal-Klassifikation: | 500 Naturwissenschaften und Mathematik > 510 Mathematik |
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| Status: | Veröffentlicht |
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| Begutachtet: | Ja, diese Version wurde begutachtet |
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| An der Universität Regensburg entstanden: | Ja |
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| Dokumenten-ID: | 75756 |
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Zusammenfassung
Optimal-order uniform-in-time H1-norm error estimates are given for semi- and full discretizations of mean curvature flow of surfaces in arbitrarily high codimension. The proposed and studied numerical method is based on a parabolic system coupling the surface flow to evolution equations for the mean curvature vector and for the orthogonal projection onto the tangent space. The algorithm uses ...
Zusammenfassung
Optimal-order uniform-in-time H1-norm error estimates are given for semi- and full discretizations of mean curvature flow of surfaces in arbitrarily high codimension. The proposed and studied numerical method is based on a parabolic system coupling the surface flow to evolution equations for the mean curvature vector and for the orthogonal projection onto the tangent space. The algorithm uses evolving surface finite elements and linearly implicit backward difference formulas. This numerical method admits a convergence analysis in the case of finite elements of polynomial degree at least 2 and backward difference formulas of orders 2 to 5. Numerical experiments in codimension 2 illustrate and complement our theoretical results.
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