Título:
Local energy estimates for the fractional Laplacian.
Otros títulos:
Coordinador:
Director:
Compilador:
Autor:
Borthagaray, Juan Pablo
Leykekhman, Dmitriy
Nochetto, Ricardo H.
Leykekhman, Dmitriy
Nochetto, Ricardo H.
Tutor:
Tipo de documento:
Preprint
Editor:
Palabras clave:
Finite elements
Error estimates
Interior error estimates
Fractional Laplacian
Error estimates
Interior error estimates
Fractional Laplacian
Descriptores:
Año de publicación:
2022
Contenido:
Resumen:
The integral fractional Laplacian of order s∈(0,1) is a nonlocal operator. It is known that solutions to the Dirichlet problem involving such an operator exhibit an algebraic boundary singularity regardless of the domain regularity. This, in turn, deteriorates the global regularity of solutions and as a result the global convergence rate of the numerical solutions. For finite element discretizations, we derive local error estimates in the Hs-seminorm and show optimal convergence rates in the interior of the domain by only assuming meshes to be shape-regular. These estimates quantify the fact that the reduced approximation error is concentrated near the boundary of the domain. We illustrate our theoretical results with several numerical examples.
Descripción:
También publicado en SIAM Journal on Numerical Analysis, vol. 59, no. 4, 2021, pp. 1918-1947.
metadata.articulos.dc.description.uri:
Editorial:
arXiv
EN:
Mathematics. Numerical Analysis (math.NA), arXiv:2005.03786v2, dec 2022, pp. 1-31.
Financiadores:
Juan Pablo Borthagaray ha sido financiado en parte por la beca DMS-1411808 de la NSF y la beca de viaje de AMS-Simons.
Citación:
Borthagaray, J., Leykekhman, D. y Nochetto, R. Local energy estimates for the fractional Laplacian. [Preprint]. Publicado en: Mathematics. Numerical Analysis (math.NA), 2022, pp. 1-31. arXiv:2005.03786v2.
Citación:
metadata.articulos.cc.license.name:
ISBN:
e-ISBN:
ISSN:
ISMN:
Otros identificadores:
Cobertura geográfica:
Cobertura temporal:
Departamento académico:
Grupo de investigación:
Licencia:
Licencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0)
Colecciones:
| Ficheros | Descripción | Tamaño | Formato | ||
|---|---|---|---|---|---|
| BLN22.pdf | Preprint | 687.09 KB | Adobe PDF |