A fractional Laplace equation: Regularity of solutions and finite element approximations

This paper deals with the integral version of the Dirichlet homogeneous fractional Laplace equation. For this problem weighted and fractional Sobolev a priori estimates are provided in terms of the Holder regularity of the data. By relying on these results, optimal order of convergence for the stand...

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Autores principales: Acosta, G., Borthagaray, J.P.
Formato: JOUR
Materias:
Finite elements
Fractional Laplacian
Graded meshes
Weighted fractional norms
Integrodifferential equations
Laplace equation
Laplace transforms
Nonlinear equations
Poisson equation
A-priori estimates
Finite element approximations
Linear finite elements
Optimal order of convergence
Regularity of solutions
Finite element method
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_00361429_v55_n2_p472_Acosta
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
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spelling todo:paper_00361429_v55_n2_p472_Acosta2023-10-03T14:47:45Z A fractional Laplace equation: Regularity of solutions and finite element approximations Acosta, G. Borthagaray, J.P. Finite elements Fractional Laplacian Graded meshes Weighted fractional norms Integrodifferential equations Laplace equation Laplace transforms Nonlinear equations Poisson equation A-priori estimates Finite element approximations Fractional Laplacian Graded meshes Linear finite elements Optimal order of convergence Regularity of solutions Weighted fractional norms Finite element method This paper deals with the integral version of the Dirichlet homogeneous fractional Laplace equation. For this problem weighted and fractional Sobolev a priori estimates are provided in terms of the Holder regularity of the data. By relying on these results, optimal order of convergence for the standard linear finite element method is proved for quasi-uniform as well as graded meshes. Some numerical examples are given showing results in agreement with the theoretical predictions. © by SIAM 2017. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_00361429_v55_n2_p472_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
Graded meshes
Weighted fractional norms
Integrodifferential equations
Laplace equation
Laplace transforms
Nonlinear equations
Poisson equation
A-priori estimates
Finite element approximations
Fractional Laplacian
Graded meshes
Linear finite elements
Optimal order of convergence
Regularity of solutions
Weighted fractional norms
Finite element method
spellingShingle Finite elements
Fractional Laplacian
Graded meshes
Weighted fractional norms
Integrodifferential equations
Laplace equation
Laplace transforms
Nonlinear equations
Poisson equation
A-priori estimates
Finite element approximations
Fractional Laplacian
Graded meshes
Linear finite elements
Optimal order of convergence
Regularity of solutions
Weighted fractional norms
Finite element method
Acosta, G.
Borthagaray, J.P.
A fractional Laplace equation: Regularity of solutions and finite element approximations
topic_facet Finite elements
Fractional Laplacian
Graded meshes
Weighted fractional norms
Integrodifferential equations
Laplace equation
Laplace transforms
Nonlinear equations
Poisson equation
A-priori estimates
Finite element approximations
Fractional Laplacian
Graded meshes
Linear finite elements
Optimal order of convergence
Regularity of solutions
Weighted fractional norms
Finite element method
description This paper deals with the integral version of the Dirichlet homogeneous fractional Laplace equation. For this problem weighted and fractional Sobolev a priori estimates are provided in terms of the Holder regularity of the data. By relying on these results, optimal order of convergence for the standard linear finite element method is proved for quasi-uniform as well as graded meshes. Some numerical examples are given showing results in agreement with the theoretical predictions. © by SIAM 2017.
format JOUR
author Acosta, G.
Borthagaray, J.P.
author_facet Acosta, G.
Borthagaray, J.P.
author_sort Acosta, G.
title A fractional Laplace equation: Regularity of solutions and finite element approximations
title_short A fractional Laplace equation: Regularity of solutions and finite element approximations
title_full A fractional Laplace equation: Regularity of solutions and finite element approximations
title_fullStr A fractional Laplace equation: Regularity of solutions and finite element approximations
title_full_unstemmed A fractional Laplace equation: Regularity of solutions and finite element approximations
title_sort fractional laplace equation: regularity of solutions and finite element approximations
url http://hdl.handle.net/20.500.12110/paper_00361429_v55_n2_p472_Acosta
work_keys_str_mv AT acostag afractionallaplaceequationregularityofsolutionsandfiniteelementapproximations
AT borthagarayjp afractionallaplaceequationregularityofsolutionsandfiniteelementapproximations
AT acostag fractionallaplaceequationregularityofsolutionsandfiniteelementapproximations
AT borthagarayjp fractionallaplaceequationregularityofsolutionsandfiniteelementapproximations
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