Finite element algorithms for nonlocal minimal graphs
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...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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AIMS Press
2022-03-01
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| Series: | Mathematics in Engineering |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/mine.2022016?viewType=HTML |
| _version_ | 1818918645100707840 |
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| author | Juan Pablo Borthagaray Wenbo Li Ricardo H. Nochetto |
| author_facet | Juan Pablo Borthagaray Wenbo Li Ricardo H. Nochetto |
| author_sort | Juan Pablo Borthagaray |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-20T00:53:15Z |
| format | Article |
| id | doaj.art-3b7234f605cc4ca8a30854469970e5f8 |
| institution | Directory Open Access Journal |
| issn | 2640-3501 |
| language | English |
| last_indexed | 2024-12-20T00:53:15Z |
| publishDate | 2022-03-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematics in Engineering |
| spelling | doaj.art-3b7234f605cc4ca8a30854469970e5f82022-12-21T19:59:11ZengAIMS PressMathematics in Engineering2640-35012022-03-014212910.3934/mine.2022016Finite element algorithms for nonlocal minimal graphsJuan Pablo Borthagaray0Wenbo Li1Ricardo H. Nochetto21. Departamento de Matemática y Estadística del Litoral, Universidad de la República, Salto, Uruguay2. Department of Mathematics, University of Tennessee, Knoxville, TN 37996, USA3. Department of Mathematics and Institute for Physical Science and Technology, University of Maryland, College Park, MD 20742, USAWe 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.https://www.aimspress.com/article/doi/10.3934/mine.2022016?viewType=HTMLnonlocal minimal surfacesfinite elementsfractional diffusion |
| spellingShingle | Juan Pablo Borthagaray Wenbo Li Ricardo H. Nochetto Finite element algorithms for nonlocal minimal graphs Mathematics in Engineering nonlocal minimal surfaces finite elements fractional diffusion |
| title | Finite element algorithms for nonlocal minimal graphs |
| title_full | Finite element algorithms for nonlocal minimal graphs |
| title_fullStr | Finite element algorithms for nonlocal minimal graphs |
| title_full_unstemmed | Finite element algorithms for nonlocal minimal graphs |
| title_short | Finite element algorithms for nonlocal minimal graphs |
| title_sort | finite element algorithms for nonlocal minimal graphs |
| topic | nonlocal minimal surfaces finite elements fractional diffusion |
| url | https://www.aimspress.com/article/doi/10.3934/mine.2022016?viewType=HTML |
| work_keys_str_mv | AT juanpabloborthagaray finiteelementalgorithmsfornonlocalminimalgraphs AT wenboli finiteelementalgorithmsfornonlocalminimalgraphs AT ricardohnochetto finiteelementalgorithmsfornonlocalminimalgraphs |