132 citations · 497 across the 66 of their papers we have counts for
5 papers · 1 filter
Fast evaluation of the Caputo fractional derivative and its applications to fractional diffusion equations
Shidong Jiang, Jiwei Zhang, Qian Zhang +1
We present an efficient algorithm for the evaluation of the Caputo fractional derivative of order , which can be expressed as a convolution of …
Superconvergence of Immersed Finite Element Methods for Interface Problems
Waixiang Cao, Xu Zhang, Zhimin Zhang
In this article, we study superconvergence properties of immersed finite element methods for the one dimensional elliptic interface problem. Due to low global regularity of the sol…
A Multilevel Correction Scheme for Nonsymmetric Eigenvalue Problems by Finite Element Methods
Hehu Xie, Zhimin Zhang
A multilevel correction scheme is proposed to solve defective and nodefective of nonsymmetric partial differential operators by the finite element method. The method includes multi…
Superconvergence points of fractional spectral interpolation
Xuan Zhao, Zhimin Zhang
We investigate superconvergence properties of the spectral interpolation involving fractional derivatives. Our interest in this superconvergence problem is, in fact, twofold: when…
Sharp Error Bounds for Piecewise Polynomial Approximation: Revisit and Application to Elliptic PDE Eigenvalue Computation
Hehu Xie, Zhimin Zhang
In this paper, we revisit approximation properties of piecewise polynomial spaces, which contain more than but not . We develop more accurate upper and…