Finite Element Methods for Fractional PDEs in Three Dimensions

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.