A short FE implementation for a 2d homogeneous Dirichlet problem of a fractional Laplacian

In Acosta etal. (2017), 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 discus...

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Autores principales: Acosta, G., Bersetche, F.M., Borthagaray, J.P.
Formato: JOUR
Materias:
Finite elements
Fractional Laplacian
Nonlocal operators
Boundary value problems
Laplace transforms
MATLAB
Dirichlet problem
Finite element codes
Non-local phenomena
Nonlocal operator
Numerical approximations
Time-dependent problem
Two dimensional spaces
Finite element method
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_08981221_v74_n4_p784_Acosta
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id todo:paper_08981221_v74_n4_p784_Acosta
record_format dspace
spelling todo:paper_08981221_v74_n4_p784_Acosta2023-10-03T15:44:00Z A short FE implementation for a 2d homogeneous Dirichlet problem of a fractional Laplacian Acosta, G. Bersetche, F.M. Borthagaray, J.P. Finite elements Fractional Laplacian Nonlocal operators Boundary value problems Laplace transforms MATLAB Dirichlet problem Finite element codes Fractional Laplacian Non-local phenomena Nonlocal operator Numerical approximations Time-dependent problem Two dimensional spaces Finite element method In Acosta etal. (2017), 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. © 2017 Elsevier Ltd Fil:Acosta, G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_08981221_v74_n4_p784_Acosta
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Finite elements
Fractional Laplacian
Nonlocal operators
Boundary value problems
Laplace transforms
MATLAB
Dirichlet problem
Finite element codes
Fractional Laplacian
Non-local phenomena
Nonlocal operator
Numerical approximations
Time-dependent problem
Two dimensional spaces
Finite element method
spellingShingle Finite elements
Fractional Laplacian
Nonlocal operators
Boundary value problems
Laplace transforms
MATLAB
Dirichlet problem
Finite element codes
Fractional Laplacian
Non-local phenomena
Nonlocal operator
Numerical approximations
Time-dependent problem
Two dimensional spaces
Finite element method
Acosta, G.
Bersetche, F.M.
Borthagaray, J.P.
A short FE implementation for a 2d homogeneous Dirichlet problem of a fractional Laplacian
topic_facet Finite elements
Fractional Laplacian
Nonlocal operators
Boundary value problems
Laplace transforms
MATLAB
Dirichlet problem
Finite element codes
Fractional Laplacian
Non-local phenomena
Nonlocal operator
Numerical approximations
Time-dependent problem
Two dimensional spaces
Finite element method
description In Acosta etal. (2017), 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. © 2017 Elsevier Ltd
format JOUR
author Acosta, G.
Bersetche, F.M.
Borthagaray, J.P.
author_facet Acosta, G.
Bersetche, F.M.
Borthagaray, J.P.
author_sort Acosta, G.
title A short FE implementation for a 2d homogeneous Dirichlet problem of a fractional Laplacian
title_short A short FE implementation for a 2d homogeneous Dirichlet problem of a fractional Laplacian
title_full A short FE implementation for a 2d homogeneous Dirichlet problem of a fractional Laplacian
title_fullStr A short FE implementation for a 2d homogeneous Dirichlet problem of a fractional Laplacian
title_full_unstemmed A short FE implementation for a 2d homogeneous Dirichlet problem of a fractional Laplacian
title_sort short fe implementation for a 2d homogeneous dirichlet problem of a fractional laplacian
url http://hdl.handle.net/20.500.12110/paper_08981221_v74_n4_p784_Acosta
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AT acostag shortfeimplementationfora2dhomogeneousdirichletproblemofafractionallaplacian
AT bersetchefm shortfeimplementationfora2dhomogeneousdirichletproblemofafractionallaplacian
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