Finite Element Approximation for the Fractional Eigenvalue Problem

The purpose of this work is to study a finite element method for finding solutions to the eigenvalue problem for the fractional Laplacian. We prove that the discrete eigenvalue problem converges to the continuous one and we show the order of such convergence. Finally, we perform some numerical exper...

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Autores principales: Borthagaray, J.P., Del Pezzo, L.M., Martínez, S.
Formato: JOUR
Materias:
Eigenvalue problem
Finite element method
Fractional Laplacian
Laplace transforms
Finding solutions
Finite element approximations
Numerical experiments
Eigenvalues and eigenfunctions
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_08857474_v77_n1_p308_Borthagaray
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id todo:paper_08857474_v77_n1_p308_Borthagaray
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spelling todo:paper_08857474_v77_n1_p308_Borthagaray2023-10-03T15:40:47Z Finite Element Approximation for the Fractional Eigenvalue Problem Borthagaray, J.P. Del Pezzo, L.M. Martínez, S. Eigenvalue problem Finite element method Fractional Laplacian Finite element method Laplace transforms Eigenvalue problem Finding solutions Finite element approximations Fractional Laplacian Numerical experiments Eigenvalues and eigenfunctions The purpose of this work is to study a finite element method for finding solutions to the eigenvalue problem for the fractional Laplacian. We prove that the discrete eigenvalue problem converges to the continuous one and we show the order of such convergence. Finally, we perform some numerical experiments and compare our results with previous work by other authors. © 2018, Springer Science+Business Media, LLC, part of Springer Nature. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_08857474_v77_n1_p308_Borthagaray
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Eigenvalue problem
Finite element method
Fractional Laplacian
Finite element method
Laplace transforms
Eigenvalue problem
Finding solutions
Finite element approximations
Fractional Laplacian
Numerical experiments
Eigenvalues and eigenfunctions
spellingShingle Eigenvalue problem
Finite element method
Fractional Laplacian
Finite element method
Laplace transforms
Eigenvalue problem
Finding solutions
Finite element approximations
Fractional Laplacian
Numerical experiments
Eigenvalues and eigenfunctions
Borthagaray, J.P.
Del Pezzo, L.M.
Martínez, S.
Finite Element Approximation for the Fractional Eigenvalue Problem
topic_facet Eigenvalue problem
Finite element method
Fractional Laplacian
Finite element method
Laplace transforms
Eigenvalue problem
Finding solutions
Finite element approximations
Fractional Laplacian
Numerical experiments
Eigenvalues and eigenfunctions
description The purpose of this work is to study a finite element method for finding solutions to the eigenvalue problem for the fractional Laplacian. We prove that the discrete eigenvalue problem converges to the continuous one and we show the order of such convergence. Finally, we perform some numerical experiments and compare our results with previous work by other authors. © 2018, Springer Science+Business Media, LLC, part of Springer Nature.
format JOUR
author Borthagaray, J.P.
Del Pezzo, L.M.
Martínez, S.
author_facet Borthagaray, J.P.
Del Pezzo, L.M.
Martínez, S.
author_sort Borthagaray, J.P.
title Finite Element Approximation for the Fractional Eigenvalue Problem
title_short Finite Element Approximation for the Fractional Eigenvalue Problem
title_full Finite Element Approximation for the Fractional Eigenvalue Problem
title_fullStr Finite Element Approximation for the Fractional Eigenvalue Problem
title_full_unstemmed Finite Element Approximation for the Fractional Eigenvalue Problem
title_sort finite element approximation for the fractional eigenvalue problem
url http://hdl.handle.net/20.500.12110/paper_08857474_v77_n1_p308_Borthagaray
work_keys_str_mv AT borthagarayjp finiteelementapproximationforthefractionaleigenvalueproblem
AT delpezzolm finiteelementapproximationforthefractionaleigenvalueproblem
AT martinezs finiteelementapproximationforthefractionaleigenvalueproblem
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