13 citations · 24 across the 11 of their papers we have counts for
11 papers
Unfitted finite element method for the quad-curl interface problem
Hailong Guo, Mingyan Zhang, Qian Zhang +1
In this paper, we introduce a novel unfitted finite element method to solve the quad-curl interface problem. We adapt Nitsche's method for curlcurl-conforming elements and double t…
Nonconforming finite elements for the Brinkman and problems on cubical meshes
Qian Zhang, Min Zhang, Zhimin Zhang
We propose two families of nonconforming elements on cubical meshes: one for the problem and the other for the Brinkman problem. The element for the $-\t…
Spurious solutions for high order curl problems
Kaibo Hu, Qian Zhang, Jiayu Han +2
We investigate numerical solutions of high order curl problems with various formulations and finite elements. We show that several classical conforming finite elements lead to spur…
A family of finite element Stokes complexes in three dimensions
Kaibo Hu, Qian Zhang, Zhimin Zhang
We construct finite element Stokes complexes on tetrahedral meshes in three-dimensional space. In the lowest order case, the finite elements in the complex have 4, 18, 16, and 1 de…
Three families of grad-div-conforming finite elements
Qian Zhang, Zhimin Zhang
Several smooth finite element de Rham complexes are constructed in three-dimensional space, which yield three families of grad-div conforming finite elements. The simplest element…
A priori and a posteriori error estimates for the quad-curl eigenvalue problem
Lixiu Wang, Qian Zhang, Jiguang Sun +1
In this paper, we propose a new family of H(curl^2)-conforming elements for the quad-curl eigenvalue problem in 2D. The accuracy of this family is one order higher than that in [32…
Curl-curl conforming elements on tetrahedra
Qian Zhang, Zhimin Zhang
In [24], we proposed H(curl^2)-conforming elements on both a triangle and a rectangle. This family of elements provides a brand new method to solve the quad-curl problem in 2 dimen…
Simple curl-curl-conforming finite elements in two dimensions
Kaibo Hu, Qian Zhang, Zhimin Zhang
We construct smooth finite element de Rham complexes in two space dimensions. This leads to three families of curl-curl conforming finite elements, two of which contain two existin…
A Minimization Method for The Double-Well Energy Functional
Qian Zhang, Long Chen, Yifeng Xu
In this paper an iterative minimization method is proposed to approximate the minimizer to the double-well energy functional arising in the phase-field theory. The method is based…
An (curl)-conforming finite element in 2D and its applications to the quad-curl problem
Qian Zhang, Lixiu Wang, Zhimin Zhang
In this paper, we first construct the (curl)-conforming finite elements both on a rectangle and a triangle. They possess some fascinating properties which have been proven by…
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 …