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

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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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Autor principal: Acosta, G.
Otros Autores: Borthagaray, J.P
Formato: Capítulo de libro
Lenguaje:Inglés
Publicado: Society for Industrial and Applied Mathematics Publications 2017
Acceso en línea:Registro en Scopus
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100 1 |a Acosta, G. 
245 1 2 |a A fractional Laplace equation: Regularity of solutions and finite element approximations 
260 |b Society for Industrial and Applied Mathematics Publications  |c 2017 
270 1 0 |m Acosta, G.; IMAS - CONICET, Departamento de Matematica, Universidad de Buenos AiresArgentina; email: gacosta@dm.uba.ar 
506 |2 openaire  |e Política editorial 
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520 3 |a 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.  |l eng 
593 |a IMAS - CONICET, Departamento de Matematica, Universidad de Buenos Aires, Buenos Aires, 1428, Argentina 
690 1 0 |a FINITE ELEMENTS 
690 1 0 |a FRACTIONAL LAPLACIAN 
690 1 0 |a GRADED MESHES 
690 1 0 |a WEIGHTED FRACTIONAL NORMS 
690 1 0 |a INTEGRODIFFERENTIAL EQUATIONS 
690 1 0 |a LAPLACE EQUATION 
690 1 0 |a LAPLACE TRANSFORMS 
690 1 0 |a NONLINEAR EQUATIONS 
690 1 0 |a POISSON EQUATION 
690 1 0 |a A-PRIORI ESTIMATES 
690 1 0 |a FINITE ELEMENT APPROXIMATIONS 
690 1 0 |a FRACTIONAL LAPLACIAN 
690 1 0 |a GRADED MESHES 
690 1 0 |a LINEAR FINITE ELEMENTS 
690 1 0 |a OPTIMAL ORDER OF CONVERGENCE 
690 1 0 |a REGULARITY OF SOLUTIONS 
690 1 0 |a WEIGHTED FRACTIONAL NORMS 
690 1 0 |a FINITE ELEMENT METHOD 
700 1 |a Borthagaray, J.P. 
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