24 citations · 112 across the 40 of their papers we have counts for
43 papers
A Parallel iterative Algorithm for primal-dual weak Galerkin Schemes
Chunmei Wang, Junping Wang
This paper presents and analyzes a parallelizable iterative procedure based on domain decomposition for primal-dual weak Galerkin (PDWG) finite element methods applied to the Poiss…
A Modified weak Galerkin finite element method for the Maxwell equations on polyhedral meshes
Chunmei Wang, Xiu Ye, Shangyou Zhang
We introduce a new numerical method for solving time-harmonic Maxwell's equations via the modified weak Galerkin technique. The inter-element functions of the weak Galerkin finite…
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…
Finite Expression Methods for Discovering Physical Laws from Data
Zhongyi Jiang, Chunmei Wang, Haizhao Yang
Nonlinear dynamics is a pervasive phenomenon observed in scientific and engineering disciplines. However, the task of deriving analytical expressions to describe nonlinear dynamics…
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…
Deep Operator Learning Lessens the Curse of Dimensionality for PDEs
Ke Chen, Chunmei Wang, Haizhao Yang
Deep neural networks (DNNs) have achieved remarkable success in numerous domains, and their application to PDE-related problems has been rapidly advancing. This paper provides an e…
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…
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…
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…
A Weak Galerkin Method for Elasticity Interface Problems
Chunmei Wang, Shangyou Zhang
This article introduces a weak Galerkin (WG) finite element method for linear elasticity interface problems on general polygonal/ployhedra partitions. The developed WG method has b…
Active Learning Based Sampling for High-Dimensional Nonlinear Partial Differential Equations
Wenhan Gao, Chunmei Wang
The deep-learning-based least squares method has shown successful results in solving high-dimensional non-linear partial differential equations (PDEs). However, this method usually…
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…
Adaptive Learning on the Grids for Elliptic Hemivariational Inequalities
Jianguo Huang, Chunmei Wang, Haoqin Wang
This paper introduces a deep learning method for solving an elliptic hemivariational inequality (HVI). In this method, an expectation minimization problem is first formulated based…
Reproducing Activation Function for Deep Learning
Senwei Liang, Liyao Lyu, Chunmei Wang +1
We propose reproducing activation functions (RAFs) to improve deep learning accuracy for various applications ranging from computer vision to scientific computing. The idea is to e…
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…
Friedrichs Learning: Weak Solutions of Partial Differential Equations via Deep Learning
Fan Chen, Jianguo Huang, Chunmei Wang +1
This paper proposes Friedrichs learning as a novel deep learning methodology that can learn the weak solutions of PDEs via a minmax formulation, which transforms the PDE problem in…
Low Regularity Primal-Dual Weak Galerkin Finite Element Methods for Ill-Posed Elliptic Cauchy Problems
Chunmei Wang
A new primal-dual weak Galerkin (PDWG) finite element method is introduced and analyzed for the ill-posed elliptic Cauchy problems with ultra-low regularity assumptions on the exac…
A Modified Primal-Dual Weak Galerkin Finite Element Method for Second Order Elliptic Equations in Non-Divergence Form
Chunmei Wang
A modified primal-dual weak Galerkin (M-PDWG) finite element method is designed for the second order elliptic equation in non-divergence form. Compared with the existing PDWG metho…
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…
A simplified primal-dual weak Galerkin finite element method for Fokker-Planck type equations
Dan Li, Chunmei Wang
A simplified primal-dual weak Galerkin (S-PDWG) finite element method is designed for the Fokker-Planck type equation with non-smooth diffusion tensor and drift vector. The discret…