Finite element methods for fractional PDEs in three dimensions

Zongze Yang; Yufeng Nie; Zhanbin Yuan; Jungang Wang

doi:10.1016/j.aml.2019.106041

Finite element methods for fractional PDEs in three dimensions

Zongze Yang
, Yufeng Nie
, Zhanbin Yuan
, Jungang Wang

数学与统计学院

Northwestern Polytechnical University Xian

科研成果: 期刊稿件 › 文章 › 同行评审

12 引用（Scopus）

摘要

This paper is a generalization of the previous work (Yang et al., 2017) to the 3-D irregular convex domains. The analytical calculation formula of fractional derivatives of finite element basis functions is given and a path searching method is developed to find the integration paths corresponding to the Gaussian points. Moreover, a template matrix is introduced to speed up the procedures. Numerical experiments on a steady problem are presented verifying the efficiency of proposed techniques.

源语言	英语
文章编号	106041
期刊	Applied Mathematics Letters
卷	100
DOI	https://doi.org/10.1016/j.aml.2019.106041
出版状态	已出版 - 2月 2020

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10.1016/j.aml.2019.106041

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title = "Finite element methods for fractional PDEs in three dimensions",

abstract = "This paper is a generalization of the previous work (Yang et al., 2017) to the 3-D irregular convex domains. The analytical calculation formula of fractional derivatives of finite element basis functions is given and a path searching method is developed to find the integration paths corresponding to the Gaussian points. Moreover, a template matrix is introduced to speed up the procedures. Numerical experiments on a steady problem are presented verifying the efficiency of proposed techniques.",

keywords = "Finite element method, Fractional derivatives, Irregular domains, Path searching method, Three dimensions",

author = "Zongze Yang and Yufeng Nie and Zhanbin Yuan and Jungang Wang",

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doi = "10.1016/j.aml.2019.106041",

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AU - Yang, Zongze

AU - Nie, Yufeng

AU - Yuan, Zhanbin

AU - Wang, Jungang

PY - 2020/2

Y1 - 2020/2

N2 - This paper is a generalization of the previous work (Yang et al., 2017) to the 3-D irregular convex domains. The analytical calculation formula of fractional derivatives of finite element basis functions is given and a path searching method is developed to find the integration paths corresponding to the Gaussian points. Moreover, a template matrix is introduced to speed up the procedures. Numerical experiments on a steady problem are presented verifying the efficiency of proposed techniques.

AB - This paper is a generalization of the previous work (Yang et al., 2017) to the 3-D irregular convex domains. The analytical calculation formula of fractional derivatives of finite element basis functions is given and a path searching method is developed to find the integration paths corresponding to the Gaussian points. Moreover, a template matrix is introduced to speed up the procedures. Numerical experiments on a steady problem are presented verifying the efficiency of proposed techniques.

KW - Finite element method

KW - Fractional derivatives

KW - Irregular domains

KW - Path searching method

KW - Three dimensions

UR - https://www.scopus.com/pages/publications/85071857407

U2 - 10.1016/j.aml.2019.106041

DO - 10.1016/j.aml.2019.106041

M3 - 文章

AN - SCOPUS:85071857407

SN - 0893-9659

VL - 100

JO - Applied Mathematics Letters

JF - Applied Mathematics Letters

M1 - 106041

ER -

Finite element methods for fractional PDEs in three dimensions

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