Finite element implementation of general triangular mesh for Riesz derivative

Autor: Daopeng Yin, Liquan Mei
Jazyk: angličtina
Rok vydání: 2021
Předmět:
Zdroj: Partial Differential Equations in Applied Mathematics, Vol 4, Iss , Pp 100188- (2021)
Druh dokumentu: article
ISSN: 2666-8181
DOI: 10.1016/j.padiff.2021.100188
Popis: 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.
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