Barrett, John W. ; Garcke, Harald 
; Nürnberg, Robert
Alternative Links zum Volltext:DOIVerlag
| Dokumentenart: | Artikel |
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| Titel eines Journals oder einer Zeitschrift: | Journal of Computational Physics |
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| Verlag: | ACADEMIC PRESS INC ELSEVIER SCIENCE |
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| Ort der Veröffentlichung: | SAN DIEGO |
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| Band: | 222 |
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| Nummer des Zeitschriftenheftes oder des Kapitels: | 1 |
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| Seitenbereich: | S. 441-467 |
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| Datum: | 2007 |
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| Institutionen: | Mathematik > Prof. Dr. Harald Garcke |
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| Identifikationsnummer: | | Wert | Typ |
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| 10.1016/j.jcp.2006.07.026 | DOI |
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| Stichwörter / Keywords: | MEAN-CURVATURE FLOW; LEVEL SET APPROACH; SURFACE-DIFFUSION; ERROR ANALYSIS; MOTION; FILMS; ELECTROMIGRATION; APPROXIMATION; COMPUTATION; FORMULATION; surface diffusion; Willmore flow; triple junctions; fourth order parabolic problem; parametric finite elements; schur complement; tangential movement |
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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: | 69345 |
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Zusammenfassung
We present a finite element approximation of motion by minus the Laplacian of curvature and related flows. The proposed scheme covers both the closed curve case, and the case of curves that are connected via triple junctions. On introducing a parametric finite element approximation, we prove stability bounds and compare our scheme with existing approaches. It turns out that the new scheme has ...
Zusammenfassung
We present a finite element approximation of motion by minus the Laplacian of curvature and related flows. The proposed scheme covers both the closed curve case, and the case of curves that are connected via triple junctions. On introducing a parametric finite element approximation, we prove stability bounds and compare our scheme with existing approaches. It turns out that the new scheme has very good properties with respect to area conservation and the equidistribution of mesh points. We state also an extension of our scheme to Willmore flow of curves and discuss possible further generalizations. (c) 2006 Elsevier Inc. All rights reserved.
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