Título:
On the convergence in H1-norm for the fractional Laplacian.
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Autor:
Borthagaray, Juan Pablo
Ciarlet Jr, Patrick
Ciarlet Jr, Patrick
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Tipo de documento:
Preprint
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Palabras clave:
Fractional Laplacian
Finite elements
Graded meshes
Finite elements
Graded meshes
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Año de publicación:
2018
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Resumen:
We consider the numerical solution of the fractional Laplacian of index s∈(1/2,1) in a bounded domain Ω with homogeneous boundary conditions. Its solution a priori belongs to the fractional order Sobolev space H˜s(Ω). For the Dirichlet problem and under suitable assumptions on the data, it can be shown that its solution is also in H1(Ω). In this case, if one uses the standard Lagrange finite element to discretize the problem, then both the exact and the computed solution belong to H1(Ω). A natural question is then whether one can obtain error estimates in H1(Ω)-norm, in addition to the classical ones that can be derived in the H˜s(Ω) energy norm. We address this issue, and in particular we derive error estimates for the Lagrange finite element solutions on both quasi-uniform and graded meshes.
Descripción:
También publicado en SIAM Journal on Numerical Analysis, vol. 57, no 4, 2019, pp. 1723-1743. DOI : 10.1137/18M122143
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arXiv
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Mathematics. Numerical Analysis (math.NA), arXiv:1810.07645v1, oct. 2018, pp. 1-19.
Financiadores:
Juan Pablo Borthagaray ha sido financiado en parte por la subvención DMS-1411808 de la NSF.
Citación:
Borthagaray, J y Ciarlet Jr, P. On the convergence in H1-norm for the fractional Laplacian. [Preprint]. Publicado en: Mathematics. Numerical Analysis (math.NA), 2018, pp 1-19. arXiv:1810.07645v1.
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Licencia Creative Commons Atribución - No Comercial - Sin Derivadas (CC - By-NC-ND 4.0)
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| Ficheros | Descripción | Tamaño | Formato | ||
|---|---|---|---|---|---|
| BC18.pdf | Preprint | 559.94 KB | Adobe PDF |