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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Bibliographic Details
Published in:	Partial differential equations in applied mathematics : a spin-off of Applied Mathematics Letters Vol. 4; p. 100188
Main Authors:	Yin, Daopeng, Mei, Liquan
Format:	Journal Article
Language:	English
Published:	Elsevier B.V 01.12.2021 Elsevier
Subjects:	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
Online Access:	Get full text
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Summary:	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