Título:
A short FE implementation for a 2d homogeneous Dirichlet problem of a fractional Laplacian
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Autor:
Acosta, Gabriel
Bersetche, Francisco M.
Borthagaray, Juan Pablo
Bersetche, Francisco M.
Borthagaray, Juan Pablo
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Tipo de documento:
Preprint
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Palabras clave:
Finite elements
Fractional Laplacian
Nonlocal operators
Fractional Laplacian
Nonlocal operators
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Año de publicación:
2017
Contenido:
Resumen:
In \cite{AcostaBorthagaray}, a complete n-dimensional finite element analysis of the homogeneous Dirichlet problem associated to a fractional Laplacian was presented. Here we provide a comprehensive and simple 2D MATLAB finite element code for such a problem. The code is accompanied with a basic discussion of the theory relevant in the context. The main program is written in about 80 lines and can be easily modified to deal with other kernels as well as with time dependent problems. The present work fills a gap by providing an input for a large number of mathematicians and scientists interested in numerical approximations of solutions of a large variety of problems involving nonlocal phenomena in two-dimensional space.
Descripción:
También publicado en Computers & Mathematics with Applications, vol. 74, no 4, 2017, pp 784-816. DOI: 10.1016/j.camwa.2017.05.026.
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Editorial:
arXiv
EN:
Mathematics. Numerical Analysis (math.NA), arXiv:1610.05558v2, may 2017, pp 1-46
Financiadores:
Este trabajo ha sido financiado parcialmente por CONICET, ANPCYT y UBA bajo las becas PIP 2014 1220130100034CO, PICT 2014-1771 y UBACYT 20020130100205BA
Citación:
Acosta, G., Bersetche, F. y Borthagaray, J. A short FE implementation for a 2d homogeneous Dirichlet problem of a fractional Laplacian. [Preprint]. Publicado en: Mathematics. Numerical Analysis (math.NA), 2017, pp 1-46. arXiv:1610.05558v2. DOI: 10.48550/arXiv.1610.05558
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Licencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0)
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| Ficheros | Descripción | Tamaño | Formato | ||
|---|---|---|---|---|---|
| ABB17.pdf | Preprint | 927.14 KB | Adobe PDF |