Blank, L. ; Garcke, H. 
; Sarbu, L. ; Styles, V.
Alternative Links zum Volltext:DOIVerlag
| Dokumentenart: | Artikel |
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| Titel eines Journals oder einer Zeitschrift: | IMA Journal of Numerical Analysis |
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| Verlag: | OXFORD UNIV PRESS |
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| Ort der Veröffentlichung: | OXFORD |
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| Band: | 33 |
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| Nummer des Zeitschriftenheftes oder des Kapitels: | 4 |
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| Seitenbereich: | S. 1126-1155 |
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| Datum: | 2013 |
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| Institutionen: | Mathematik > Prof. Dr. Harald Garcke |
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| Identifikationsnummer: | | Wert | Typ |
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| 10.1093/imanum/drs039 | DOI |
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| Stichwörter / Keywords: | FINITE-ELEMENT APPROXIMATION; PHASE-FIELD MODEL; NUMERICAL SIMULATIONS; IMAGE SEGMENTATION; BOUNDARY MOTION; NEWTON METHOD; EQUATION; CONSTRAINTS; INEQUALITY; SEPARATION; Allen-Cahn systems; nonlocal constraints; variational inequality; vector-valued obstacle problems; primal-dual active set method; semismooth Newton method |
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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: | 62235 |
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Zusammenfassung
We show the existence and uniqueness of a solution for the nonlocal vector-valued Allen-Cahn variational inequality in a formulation involving Lagrange multipliers for local and nonlocal constraints. Furthermore, we propose and analyse a primal-dual active set (PDAS) method for local and nonlocal vector-valued Allen-Cahn variational inequalities. The local convergence behaviour of the PDAS ...
Zusammenfassung
We show the existence and uniqueness of a solution for the nonlocal vector-valued Allen-Cahn variational inequality in a formulation involving Lagrange multipliers for local and nonlocal constraints. Furthermore, we propose and analyse a primal-dual active set (PDAS) method for local and nonlocal vector-valued Allen-Cahn variational inequalities. The local convergence behaviour of the PDAS algorithm is studied by interpreting the approach as a semismooth Newton method and numerical simulations are presented demonstrating its efficiency.
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