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 2ndirections in n−dimension space, which the difficulties for computation of variation formula rightly bother us. In this pape...

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Autores principales:	Daopeng Yin, Liquan Mei
Formato:	article
Lenguaje:	EN
Publicado:	Elsevier 2021
Materias:	Riesz fractional derivative Finite element methods Algorithm implementation Stiffness matrix Applied mathematics. Quantitative methods T57-57.97
Acceso en línea:	https://doaj.org/article/1f2b57c11c3143749222927f047d36ad
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id	oai:doaj.org-article:1f2b57c11c3143749222927f047d36ad
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spelling	oai:doaj.org-article:1f2b57c11c3143749222927f047d36ad2021-11-14T04:35:59ZFinite element implementation of general triangular mesh for Riesz derivative2666-818110.1016/j.padiff.2021.100188https://doaj.org/article/1f2b57c11c3143749222927f047d36ad2021-12-01T00:00:00Zhttp://www.sciencedirect.com/science/article/pii/S266681812100098Xhttps://doaj.org/toc/2666-8181In 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 2ndirections 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.Daopeng YinLiquan MeiElsevierarticleRiesz fractional derivativeFinite element methodsAlgorithm implementationStiffness matrixApplied mathematics. Quantitative methodsT57-57.97ENPartial Differential Equations in Applied Mathematics, Vol 4, Iss , Pp 100188- (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Riesz fractional derivative Finite element methods Algorithm implementation Stiffness matrix Applied mathematics. Quantitative methods T57-57.97
spellingShingle	Riesz fractional derivative Finite element methods Algorithm implementation Stiffness matrix Applied mathematics. Quantitative methods T57-57.97 Daopeng Yin Liquan Mei Finite element implementation of general triangular mesh for Riesz derivative
description	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 2ndirections 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.
format	article
author	Daopeng Yin Liquan Mei
author_facet	Daopeng Yin Liquan Mei
author_sort	Daopeng Yin
title	Finite element implementation of general triangular mesh for Riesz derivative
title_short	Finite element implementation of general triangular mesh for Riesz derivative
title_full	Finite element implementation of general triangular mesh for Riesz derivative
title_fullStr	Finite element implementation of general triangular mesh for Riesz derivative
title_full_unstemmed	Finite element implementation of general triangular mesh for Riesz derivative
title_sort	finite element implementation of general triangular mesh for riesz derivative
publisher	Elsevier
publishDate	2021
url	https://doaj.org/article/1f2b57c11c3143749222927f047d36ad
work_keys_str_mv	AT daopengyin finiteelementimplementationofgeneraltriangularmeshforrieszderivative AT liquanmei finiteelementimplementationofgeneraltriangularmeshforrieszderivative
_version_	1718429884067348480

Finite element implementation of general triangular mesh for Riesz derivative

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