Finite element implementation of general triangular mesh for Riesz derivative

In this work, we will study a calculation method of variation formula with Riesz fractional derivative. As far as we know, Riesz derivative is a non-local operator including 2n directions in n−dimension space, which the difficulties for computation of variation formula rightly bother us. In this pap...

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Vydáno v:Partial differential equations in applied mathematics : a spin-off of Applied Mathematics Letters Ročník 4; s. 100188
Hlavní autoři: Yin, Daopeng, Mei, Liquan
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier B.V 01.12.2021
Elsevier
Témata:
Algorithm implementation
Finite element methods
Riesz fractional derivative
Stiffness matrix
Stiffness matrix
Algorithm implementation
Finite element methods
Riesz fractional derivative
ISSN:2666-8181, 2666-8181
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Shrnutí:In this work, we will study a calculation method of variation formula with Riesz fractional derivative. As far as we know, Riesz derivative is a non-local operator including 2n directions in n−dimension space, which the difficulties for computation of variation formula rightly bother us. In this paper, we will give an accurate method to cope with element of the stiffness matrix using polynomial basis function in the general domain meshed by unstructured triangle and the proof of diagonal dominance for Riesz fractional stiffness matrix. This method can be utilized to general fractional differential equation with Riesz derivative, which especially suitable for β close to 0.5 or 1.
ISSN:2666-8181
2666-8181
DOI:10.1016/j.padiff.2021.100188