Título:
Finite element algorithms for nonlocal minimal graphs
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Autor:
Borthagaray, Juan Pablo
Li, Wenbo
Nochetto, Ricardo
Li, Wenbo
Nochetto, Ricardo
Tutor:
Tipo de documento:
Artículo
Editor:
Palabras clave:
Nonlocal minimal surfaces
Finite elements
Fractional diffusion
Finite elements
Fractional diffusion
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Año de publicación:
2022
Contenido:
Resumen:
We discuss computational and qualitative aspects of the fractional Plateau and the prescribed fractional mean curvature problems on bounded domains subject to exterior data being a subgraph. We recast these problems in terms of energy minimization, and we discretize the latter with piecewise linear finite elements. For the computation of the discrete solutions, we propose and study a gradient flow and a Newton scheme, and we quantify the effect of Dirichlet data truncation. We also present a wide variety of numerical experiments that illustrate qualitative and quantitative features of fractional minimal graphs and the associated discrete problems.
Descripción:
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Editorial:
AIMS Press
EN:
Mathematics in Engineering, 2022, 4(2): 1–29
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Citación:
Borthagaray, J, Li, W y Nochetto, R. "Finite element algorithms for nonlocal minimal graphs". Mathematics in Engineering. [en línea] 2022, 4(2): 1–29. 29 h. DOI: 10.3934/mine.2022016
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ISSN:
2640-3501
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Licencia:
Licencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0)
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| 60f6c0b5ba35de03c3cfb9d4.pdf | — | 2.45 MB | Adobe PDF |