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arXiv · 1811.03339

Finite Element Methods for Fractional PDEs in Three Dimensions

Zongze Yang·Zhanbin Yuan·Yufeng Nie·Jungang Wang
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Abstract

This paper is a generalization of the previous work (Yang et.al, J. Comput. Phys. 330 (2017), 863-883) to the 3-D irregular convex domains. The analytical calculation formula of fractional derivatives of finite element basis functions are 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.

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Zongze Yang, Zhanbin Yuan, Yufeng Nie, Jungang Wang. 2019-09-07. Finite Element Methods for Fractional PDEs in Three Dimensions. https://doi.org/10.1016/j.aml.2019.106041

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