8 citations · 25 across the 21 of their papers we have counts for
21 papers
Low-degree robust Hellinger-Reissner finite element schemes for planar linear elasticity with symmetric stress tensors
Shuo Zhang
In this paper, we study the construction of low-degree robust finite element schemes for planar linear elasticity on general triangulations. Firstly, we present a low-degree noncon…
A lowest-degree strictly conservative finite element scheme for incompressible Stokes problem on general triangulations
Wenjia Liu, Shuo Zhang
In this paper, we propose a finite element pair for incompressible Stokes problem. The pair uses a slightly enriched piecewise linear polynomial space for velocity and piecewise co…
A low-degree strictly conservative finite element method for incompressible flows
Huilan Zeng, Chen-Song Zhang, Shuo Zhang
In this paper, a new finite element pair is proposed for incompressible fluid. For this pair, the discrete inf-sup condition and the discrete Korn's inequality hold o…
A simple low-degree optimal finite element scheme for the elastic transmission eigenvalue problem
Yingxia Xi, Xia Ji, Shuo Zhang
The paper presents a finite element scheme for the elastic transmission eigenvalue problem written as a fourth order eigenvalue problem. The scheme uses piecewise cubic polynomials…
Lowest-degree robust finite element scheme for a fourth-order elliptic singular perturbation problem on rectangular grids
Huilan Zeng, Chen-Song Zhang, Shuo Zhang
In this paper, a piecewise quadratic nonconforming finite element method on rectangular grids for a fourth-order elliptic singular perturbation problem is presented. This proposed…
Lowest-degree piecewise polynomial de Rham complex on general quadrilateral grids
Qimeng Quan, Xia Ji, Shuo Zhang
This paper is devoted to the construction of finite elements on grids that consist of general quadrilaterals not limited in parallelograms. Two finite elements defined as Ciarlet's…
A high accuracy nonconforming finite element scheme for Helmholtz transmission eigenvalue problem
Yingxia Xi, Xia Ji, Shuo Zhang
In this paper, we consider a cubic nonconforming finite element scheme which does not correspond to a locally defined finite element with Ciarlets triple but ad…
An optimal piecewise cubic nonconforming finite element scheme for the planar biharmonic equation on general triangulations
Shuo Zhang
This paper presents a nonconforming finite element scheme for the planar biharmonic equation which applis piecewise cubic polynomials () and possesses conve…
Optimal quadratic element on rectangular grids for problems
Huilan Zeng, Chensong Zhang, Shuo Zhang
In this paper, a piecewise quadratic finite element method on rectangular grids for the problems is presented. The proposed method can be viewed as a reduced rectangular Morl…
On optimal finite element schemes for biharmonic equation
Shuo Zhang
In this paper, two nonconforming finite element schemes that use piecewise cubic and piecewise quartic polynomials respectively are constructed for the planar biharmonic equation w…
Nonstandard finite element de Rham complexes on cubical meshes
Andrew Gillette, Kaibo Hu, Shuo Zhang
We propose two general operations on finite element differential complexes on cubical meshes that can be used to construct and analyze sequences of "nonstandard" convergent methods…
Minimal consistent finite element space for the biharmonic equation on quadrilateral grids
Shuo Zhang
In this paper, a finite element space is presented on quadrilateral grids which can provide consistent discretization for the biharmonic equations. The space consists of piecewise…
A Multi-level Mixed Element scheme of the two dimensional helmholtz transmission eigenvalue problem
Y. Xi, X. Ji, S. Zhang
In this paper, we present a multi-level mixed element scheme for the Helmholtz transmission eigenvalue problem on polygonal domains that are not necessarily able to be covered by r…
Stable mixed element schemes for plate models on multiply-connected domains
Shuo Zhang
In this paper, we study the mixed element schemes of the Reissner-Mindlin plate model and the Kirchhoff plate model in multiply-connected domains. By a regular decomposition of $H_…
Decoupled mixed element schemes for fourth order problems
Shuo Zhang
In this paper, we study decoupled mixed element schemes for fourth order problems. A general process is designed such that an elliptic problem on high-regularity space is transform…
Regular decomposition and a framework of order reducd methods for fourth order problems
Shuo Zhang
This paper is devoted to the construction of order reduced method of fourth order problems. A framework is presented such that a problem on a high-regularity space can be deduced i…
Amiable mixed schemes for fourth order curl equations
Shuo Zhang
In this paper, amiable mixed schemes are presented for two variants of fourth order curl equations. Specifically, mixed formulations for the problems are constructed, which are wel…
A Multi-level Mixed Element Method for the Eigenvalue Problem of Biharmonic Equation
Shuo Zhang, Yingxia Xi, Xia Ji
In this paper, we discuss approximating the eigenvalue problem of biharmonic equation. We first present an equivalent mixed formulation which admits amiable nested discretization.…
Convergence analysis of the rectangular Morley element scheme for second order problem in arbitrary dimensions
XiangYun Meng, XueQin Yang, Shuo Zhang
In this paper, we present the convergence analysis of the rectangular Morley element scheme utilised on the second order problem in arbitrary dimensions. Specifically, we prove tha…
Capacity of the Adini element for biharmonic equations
Jun Hu, Xueqin Yang, Shuo Zhang
This paper is devoted to the convergence analysis of the Adini element scheme for the fourth order problem in arbitrary dimension. We prove that, the Adini element scheme is $\math…
Stable finite element pair for Stokes problem and discrete Stokes complex on quadrilateral grids
Shuo Zhang
In this paper, we first construct a nonconforming finite element pair for the incompressible Stokes problem on quadrilateral grids, and then construct a discrete Stokes complex ass…