1.3k citations
Counting papers with at most 25 authors, so collaboration author lists do not stand in for the people here.
- University of Arkansas at FayettevilleUS17 papers
- University of DelawareUS16 papers
- U.S. National Science FoundationUS15 papers
- Iowa State UniversityUS13 papers
- Purdue University West LafayetteUS12 papers
- Center for Astrophysics Harvard & SmithsonianUS11 papers
- Michigan State UniversityUS11 papers
- Division of Mathematical SciencesUS10 papers
- University of California, Los AngelesUS10 papers
- Washington University in St. LouisUS10 papers
- DePauw UniversityUS9 papers
- Galway-Mayo Institute of TechnologyIE9 papers
36 papers · 1 filter
A Posteriori Estimates of Taylor-Hood Element for Stokes Problem Using Auxiliary Subspace Techniques
Jiachuan Zhang, Ran Zhang, Xiaoshen Wang
Based on the auxiliary subspace techniques, a hierarchical basis a posteriori error estimator is proposed for the Stokes problem in two and three dimensions. For the error estimato…
A stabilizer free, pressure robust, and superconvergence weak Galerkin finite element method for the Stokes Equations on polytopal mesh
Lin Mu, Xiu Ye, Shangyou Zhang
In this paper, we propose a new stabilizer free and pressure robust WG method for the Stokes equations with super-convergence on polytopal mesh in the primary velocity-pressure for…
A polynomial lifting operator on polygons and polyhedrons
Xiu Ye, Shangyou Zhang
A polynomial lifting operator is defined on polygons and polyhedrons. It lifts discontinuous polynomials inside the polygon/polyhedron and on the faces to a one-piece $P_…
A stabilizer free WG Method for the Stokes Equations with order two superconvergence on polytopal mesh
Xiu Ye, Shangyou Zhang
A stabilizer free WG method is introduced for the Stokes equations with superconvergence on polytopal mesh in primary velocity-pressure formulation. Convergence rates two order hig…
A stabilizer free weak Galerkin finite element method on polytopal mesh: Part II
Xiu Ye, Shangyou Zhang
A stabilizer free weak Galerkin (WG) finite element method on polytopal mesh has been introduced in Part I of this paper (J. Comput. Appl. Math, 371 (2020) 112699. arXiv:1906.06634…
A conforming discontinuous Galerkin finite element method for the Stokes problem on polytopal meshes
Xiu Ye, Shangyou Zhang
A new discontinuous Galerkin finite element method for the Stokes equations is developed in the primary velocity-pressure formulation. This method employs discontinuous polynomials…
A stabilizer-free pressure-robust finite element method for the Stokes equations
Xiu Ye, Shangyou Zhang
In this paper, we introduce a new finite element method for solving the Stokes equations in the primary velocity-pressure formulation. This method employs finite elements…
De Rham Complexes for Weak Galerkin Finite Element Spaces
Chunmei Wang, Junping Wang, Xiu Ye +1
Two de Rham complex sequences of the finite element spaces are introduced for weak finite element functions and weak derivatives developed in the weak Galerkin (WG) finite element…
A new weak gradient for the stabilizer free weak Galerkin method with polynomial reduction
Xiu Ye, Shangyou Zhang
The weak Galerkin (WG) finite element method is an effective and flexible general numerical technique for solving partial differential equations. It is a natural extension of the c…
Numerical investigation on weak Galerkin finite elements
Xiu Ye, Shangyou Zhang
The weak Galerkin (WG) finite element method is an effective and flexible general numerical technique for solving partial differential equations. The novel idea of weak Galerkin fi…
A stabilizer free weak Galerkin element method with supercloseness of order two
Ahmed Al-Taweel, Xiaoshen Wang, Xiu Ye +1
The weak Galerkin (WG) finite element method is an effective and flexible general numerical techniques for solving partial differential equations. A simple weak Galerkin finite ele…
The lowest-order stabilizer free Weak Galerkin Finite Element Method
Ahmed Al-Taweel, Xiaoshen Wang
Recently, a new stabilizer free weak Galerkin method (SFWG) is proposed, which is easier to implement and more efficient. The main idea is that by letting for some $j…
A stabilizer free weak Galerkin method for the Biharmonic Equation on Polytopal Meshes
Xiu Ye, Shangyou Zhang
A new stabilizer free weak Galerkin (WG) method is introduced and analyzed for the biharmonic equation. Stabilizing/penalty terms are often necessary in the finite element formulat…
On stabilizer-free weak Galerkin finite element methods on polytopal meshes
Xiu Ye, Shangyou Zhang
A stabilizing/penalty term is often used in finite element methods with discontinuous approximations to enforce connection of discontinuous functions across element boundaries. Rem…
A conforming discontinuous Galerkin finite element method: Part II
Xiu Ye, Shangyou Zhang
A conforming discontinuous Galerkin (DG) finite element method has been introduced in [21] on simplicial meshes, which has the flexibility of using discontinuous approximation and…
A note on the optimal degree of the weak gradient of the stabilizer free weak Galerkin finite element method
Ahmed Al-Taweel, Xiaoshen Wang
Recently, a new stabilizer free weak Galerkin method (SFWG) is proposed, which is easier to implement. The idea is to raise the degree of polynomials j for computing weak gradient.…
The Basics of Weak Galerkin Finite Element Methods
Junping Wang, Xiu Ye
The goal of this article is to clarify some misunderstandings and inappropriate claims made in [6] regarding the relation between the weak Galerkin (WG) finite element method and t…
A simple finite element method for the Stokes equations
Lin Mu, Xiu Ye
The goal of this paper is to introduce a simple finite element method to solve the Stokes and the Navier-Stokes equations. This method is in primal velocity-pressure formulation an…
Effective Implementation of the Weak Galerkin Finite Element Methods for the Biharmonic Equation
Lin Mu, Junping Wang, Xiu Ye
The weak Galerkin (WG) methods have been introduced in the references [11, 16] for solving the biharmonic equation. The purpose of this paper is to develop an algorithm to implemen…
A Weak Galerkin Finite Element Scheme for solving the stationary Stokes Equations
Ruishu Wang, Xiaoshen Wang, Qilong Zhai +1
A weak Galerkin (WG) finite element method for solving the stationary Stokes equations in two- or three- dimensional spaces by using discontinuous piecewise polynomials is develope…
A weak Galerkin finite element scheme with boundary continuity for second-order elliptic problems
Qilong Zhai, Xiu Ye, Ruishu Wang +1
A new weak Galerkin (WG) finite element method for solving the second-order elliptic problems on polygonal meshes by using polynomials of boundary continuity is introduced and anal…
A Hybridized Formulation for the Weak Galerkin Mixed Finite Element Method
Lin Mu, Junping Wang, Xiu Ye
This paper presents a hybridized formulation for the weak Galerkin mixed finite element method (WG-MFEM) which was introduced and analyzed for second order elliptic equations. The…
A Hybridized Weak Galerkin Finite Element Scheme for the Stokes Equations
Qilong Zhai, Ran Zhang, Xiaoshen Wang
In this paper a hybridized weak Galerkin (HWG) finite element method for solving the Stokes equations in the primary velocity-pressure formulation is introduced. The WG method uses…
An auxiliary space multigrid preconditioner for the weak Galerkin method
Long Chen, Junping Wang, Yanqiu Wang +1
In this paper, the authors constructed an auxiliary space multigrid preconditioner for the weak Galerkin finite element method for second-order diffusion equations, discretized on…