138 citations · 489 across the 53 of their papers we have counts for
56 papers
Beyond Taylor: Divergence-Based Functional Expansions and Their Application to Numerical Integration
Junping Wang
This paper introduces a new functional expansion framework that extends classical ideas beyond the Taylor series. Unlike traditional Taylor expansions based on local polynomial app…
A Generalized Weak Galerkin Method for Linear Elasticity with Nonpolynomial Approximations
Junping Wang, Yue Wang
This paper presents a generalized weak Galerkin (gWG) finite element method for linear elasticity problems on general polygonal and polyhedral meshes. The proposed framework is fle…
High Order Morley Elements for Biharmonic Equations on Polytopal Partitions
Dan Li, Chunmei Wang, Junping Wang +1
This paper introduces an extension of the Morley element for approximating solutions to biharmonic equations. Traditionally limited to piecewise quadratic polynomials on triangular…
Generalized weak Galerkin finite element methods for second order elliptic problems
Dan Li, Chunmei Wang, Junping Wang +1
This article proposes and analyzes the generalized weak Galerkin ({\rm g}WG) finite element method for the second order elliptic problem. A generalized discrete weak gradient opera…
Generalized Weak Galerkin Finite Element Methods for Biharmonic Equations
Dan Li, Chunmei Wang, Junping Wang
The generalized weak Galerkin (gWG) finite element method is proposed and analyzed for the biharmonic equation. A new generalized discrete weak second order partial derivative is i…
An -primal-dual finite element method for first-order transport problems
Dan Li, Chunmei Wang, Junping Wang
A new -primal-dual weak Galerkin method (-PDWG) with is proposed for the first-order transport problems. The existence and uniqueness of the -PDWG numerical so…
Curved Elements in Weak Galerkin Finite Element Methods
Dan Li, Chunmei Wang, Junping Wang
A mathematical analysis is established for the weak Galerkin finite element methods for the Poisson equation with Dirichlet boundary value when the curved elements are involved on…
Weak Galerkin Finite Element Methods for Quad-Curl Problems
Chunmei Wang, Junping Wang, Shangyou Zhang
This article introduces a weak Galerkin (WG) finite element method for quad-curl problems in three dimensions. It is proved that the proposed WG method is stable and accurate in an…
An Extension of the Morley Element on General Polytopal Partitions Using Weak Galerkin Methods
Dan Li, Chunmei Wang, Junping Wang
This paper introduces an extension of the well-known Morley element for the biharmonic equation, extending its application from triangular elements to general polytopal elements us…
A Generalized Weak Galerkin method for Oseen equation
Wenya Qi, Padmanabhan Seshaiyer, Junping Wang
In this work, the authors introduce a generalized weak Galerkin (gWG) finite element method for the time-dependent Oseen equation. The generalized weak Galerkin method is based on…
An - Primal-Dual Weak Galerkin method for div-curl Systems
Waixiang Cao, Chunmei Wang, Junping Wang
This paper presents a new -primal-dual weak Galerkin (PDWG) finite element method for the div-curl system with the normal boundary condition for . Two crucial features fo…
Generalized Weak Galerkin Methods For Stokes Equations
W. Qi, P. Seshaiyer, J. Wang
A new weak Galerkin finite element method, called generalized weak Galerkin method ({g}WG), is introduced for Stokes equations in this paper by using a new definition of the weak g…
A parallel iterative procedure for weak Galerkin methods for second order elliptic problems
Chunmei Wang, Junping Wang, Shangyou Zhang
A parallelizable iterative procedure based on domain decomposition is presented and analyzed for weak Galerkin finite element methods for second order elliptic equations. The conve…
An - Primal-Dual Weak Galerkin Method for Convection-Diffusion Equations
Waixiang Cao, Chunmei Wang, Junping Wang
In this article, the authors present a new - primal-dual weak Galerkin method (-PDWG) for convection-diffusion equations with . The existence and uniqueness of the n…
An -weak Galerkin method for second order elliptic equations in non-divergence form
Waixiang Cao, Junping Wang, Yuesheng Xu
This article presents a new primal-dual weak Galerkin method for second order elliptic equations in non-divergence form. The new method is devised as a constrained -optimizati…
A New Numerical Method for Div-Curl Systems with Low Regularity Assumptions
Shuhao Cao, Chunmei Wang, Junping Wang
This paper presents a numerical method for div-curl systems with normal boundary conditions by using a finite element technique known as primal-dual weak Galerkin (PDWG). The PDWG…
A New Primal-Dual Weak Galerkin Method for Elliptic Interface Problems with Low Regularity Assumptions
Waixiang Cao, Chunmei Wang, Junping Wang
This article introduces a new primal-dual weak Galerkin (PDWG) finite element method for second order elliptic interface problems with ultra-low regularity assumptions on the exact…
Finite element method with the total stress variable for Biot's consolidation model
Wenya Qi, Padmanabhan Seshaiyer, Junping Wang
In this work, semi-discrete and fully-discrete error estimates are derived for the Biot's consolidation model described using a three-field finite element formulation. The fields i…
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 Primal-Dual Weak Galerkin Method for Div-Curl Systems with low-regularity solutions
Yujie Liu, Junping Wang
This article presents a new primal-dual weak Galerkin finite element method for the div-curl system with tangential boundary conditions and low-regularity assumptions on the soluti…
A Locking-Free Finite Element Method for Linear Elasticity Equations on Polytopal Partitions
Yujie Liu, Junping Wang
This article presents a finite element method for boundary value problems for linear elasticity equations. The new method makes use of piecewise constant approximating functi…
A Primal-dual weak Galerkin finite element method for linear convection equations in non-divergence form
Dan Li, Chunmei Wang, Junping Wang
A new primal-dual weak Galerkin (PD-WG) finite element method was developed and analyzed in this article for first-order linear convection equations in non-divergence form. The PD-…
A primal-dual finite element method for first-order transport problems
Chunmei Wang, Junping Wang
This article devises a new numerical method for first-order transport problems by using the primal-dual weak Galerkin (PD-WG) finite element method recently developed in scientific…
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…