A Fractional Laplace Equation: Regularity of Solutions and Finite Element Approximations
By Gabriel Acosta, Juan Pablo Borthagaray. SIAM Journal on Numerical Analysis, 2015
306 citations recorded by the source corpus.
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.
Subfields: Applied Mathematics, Mechanics of Materials, Modeling and Simulation
View Paper: https://www.semanticscholar.org/paper/21dc66abb453524947c52484b4597f41e6c9fef4
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In Applied Mathematics
- Lexing Ying
- Victor Minden
- Zhiping Mao
- Mark Ainsworth
- Xiaoning Zheng
- G. Em Karniadakis
- Fangying Song
- Christian Glusa
In Mechanics of Materials
- G. Em Karniadakis
- Guofei Pang
- Mark Ainsworth
- Mark M. Meerschaert
- Wei Cai
- Fawang Liu
- Ian L Turner
- Vo Anh
In Modeling and Simulation
- G. Em Karniadakis
- Guofei Pang
- Zhiping Mao
- Mark Ainsworth
- Lexing Ying
- Victor Minden
- Fangying Song
- Wei Cai
Citations in the corpus
- A Simple Solver for the Fractional Laplacian in Multiple Dimensions (2018, background): “Other similar work on efficient solution of fractional Laplacian systems using fast preconditioned iterative methods includes Pang and Sun [41] and Wang and collaborators [17–19 , Another family of approaches on discretizing the fractional Laplacian operator is based on finite elements [2,4,6–8,48,49].”
- What is the fractional Laplacian? A comparative review with new results (2018, methodology): “For the case of zero exterior Dirichlet condition g ≡ 0 in (28), finite element algorithms have been developed in [69], [71], and in particular the adaptive finite element scheme of [72] has been used for the computations of this paper.”
- Nonlocal discrete diffusion equations and the fractional discrete Laplacian, regularity and applications (2016, unknown): “The large literature includes numerical approximations of different sorts, see for example [1, 2, 8, 12, 13, 18] and references therein.”