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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Veröffentlicht in:Partial differential equations in applied mathematics : a spin-off of Applied Mathematics Letters Jg. 4; S. 100188
Hauptverfasser: Yin, Daopeng, Mei, Liquan
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier B.V 01.12.2021
Elsevier
Schlagworte:
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-Zugang:Volltext
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Zusammenfassung: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