132 citations · 497 across the 66 of their papers we have counts for
66 papers
Partition-Insensitive Parallel ADMM Algorithm for High-dimensional Linear Models
Xiaofei Wu, Jiancheng Jiang, Zhimin Zhang
The parallel alternating direction method of multipliers (ADMM) algorithms have gained popularity in statistics and machine learning due to their efficient handling of large sample…
-robust error estimates of general non-uniform time-step numerical schemes for reaction-subdiffusion problems
Jiwei Zhang, Zhimin Zhang, Chengchao Zhao
Numerous error estimates have been carried out on various numerical schemes for subdiffusion equations. Unfortunately most error bounds suffer from a factor or ,…
Error estimates of invariant-preserving difference schemes for the rotation-two-component Camassa--Holm system with small energy
Qifeng Zhang, Jiyuan Zhang, Zhimin Zhang
A rotation-two-component Camassa-Holm (R2CH) system was proposed recently to describe the motion of shallow water waves under the influence of gravity. This is a highly nonlinear a…
Nonconforming finite element approximations and the analysis of Nitsche's method for a singularly perturbed quad-curl problem in three dimensions
Baiju Zhang, Zhimin Zhang
We introduce and analyze a robust nonconforming finite element method for a three dimensional singularly perturbed quad-curl model problem. For the solution of the model problem, w…
A new family of nonconforming elements with -continuity for the three-dimensional quad-curl problem
Baiju Zhang, Zhimin Zhang
We propose and analyze a new family of nonconforming finite elements for the three-dimensional quad-curl problem. The proposed finite element spaces are subspaces of $\pmb{H}(\math…
An hp-version interior penalty discontinuous Galerkin method for the quad-curl eigenvalue problem
Jiayu Han, Zhimin Zhang
An hp-version interior penalty discontinuous Galerkin (IPDG) method under nonconforming meshes is proposed to solve the quad-curl eigenvalue problem. We prove well-posedness of the…
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…
Some mathematical aspects of Anderson localization: boundary effect, multimodality, and bifurcation
Chen Jia, Ziqi Liu, Zhimin Zhang
Anderson localization is a famous wave phenomenon that describes the absence of diffusion of waves in a disordered medium. Here we generalize the landscape theory of Anderson local…
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…
FE-Holomorphic Operator Function Method for Nonlinear Plate Vibrations with Elastically Added Masses
Xiangying Pang, Jiguang Sun, Zhimin Zhang
Vibrations of structures subjected to concentrated point loads have many applications in mechanical engineering. Experiments are expensive and numerical methods are often used for…
Solving Biharmonic Eigenvalue Problem With Navier Boundary Condition Via Poisson Solvers On Non-Convex Domains
Baiju Zhang, Hengguang Li, Zhimin Zhang
It is well known that the usual mixed method for solving the biharmonic eigenvalue problem by decomposing the operator into two Laplacians may generate spurious eigenvalues on non-…
Sparse Spectral-Galerkin Method on An Arbitrary Tetrahedron Using Generalized Koornwinder Polynomials
Lueling Jia, Huiyuan Li, Zhimin Zhang
In this paper, we propose a sparse spectral-Galerkin approximation scheme for solving the second-order partial differential equations on an arbitrary tetrahedron. Generalized Koorn…
H()-conforming quadrilateral spectral element method for quad-curl problems
Lixiu Wang, Weikun Shan, Huiyuan Li +1
In this paper, we propose an -conforming quadrilateral spectral element method to solve quad-curl problems. Starting with generalized Jacobi polynomials, we first…
A -conforming Petrov-Galerkin method for convection-diffusion equations and superconvergence ananlysis over rectangular meshes
Waixiang Cao, Lueling Jia, Zhimin Zhang
In this paper, a new -conforming Petrov-Galerkin method for convection-diffusion equations is designed and analyzed. The trail space of the proposed method is a -conformi…
Unconditionally optimal convergence of an energy-conserving and linearly implicit scheme for nonlinear wave equations
Waixiang Cao, Dongfang Li, Zhimin Zhang
In this paper, we present and analyze an energy-conserving and linearly implicit scheme for solving the nonlinear wave equations. Optimal error estimates in time and superconvergen…
Mesh-robustness of an energy stable BDF2 scheme with variable steps for the Cahn-Hilliard model
Hong-lin Liao, Bingquan Ji, Lin Wang +1
The two-step backward differential formula (BDF2) with unequal time-steps is applied to construct an energy stable convex-splitting scheme for the Cahn-Hilliard model. We focus on…
A finite element method for the biharmonic problem with Navier boundary conditions in a polygonal domain
Hengguang Li, Peimeng Yin, Zhimin Zhang
In this paper, we study the biharmonic equation with the Navier boundary conditions in a polygonal domain. In particular, we propose a method that effectively decouples the 4th-ord…
Efficient shifted fractional trapezoidal rule for subdiffusion problems with nonsmooth solutions on uniform meshes
Baoli Yin, Yang Liu, Hong Li +1
This article devotes to developing robust but simple correction techniques and efficient algorithms for a class of second-order time stepping methods, namely the shifted fractional…
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…
Finite Element Calculation of Photonic Band Structures for Frequency Dependent Materials
Wenqiang Xiao, Bo Gong, Jiguang Sun +1
We consider the calculation of the band structure of frequency dependent photonic crystals. The associated eigenvalue problem is nonlinear and it is challenging to develop effectiv…
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…