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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Detalles Bibliográficos
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
Descripción
Sumario: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.

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