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

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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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Detalles Bibliográficos
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
Descripción
Sumario: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

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