12 papers · 1 filter
A Least-Squares Weak Galerkin Method for the Biharmonic Cauchy Problem
Chunmei Wang, Shangyou Zhang
We develop a least-squares weak Galerkin (LS-WG) finite element method for the Cauchy problem of the biharmonic equation. The proposed approach reformulates the fourth-order equati…
A Least Squares Weak Galerkin Framework for Linear Elasticity on Polytopal Meshes
Chunmei Wang, Shangyou Zhang
This paper develops and analyzes a least-squares weak Galerkin (LS-WG) finite element method for linear elasticity. By employing weak differential operators, specifically the weak…
A Least Squares Weak Galerkin Finite Element Method for Fokker-Planck Type Equations
Chunmei Wang, Shangyou Zhang
This paper presents a least squares weak Galerkin (LS-WG) finite element method for a class of second order elliptic equations of Fokker-Planck type. To address the numerical chall…
Solving the Stokes Equations via a Least Squares Weak Galerkin Method
Chunmei Wang, Shangyou Zhang
We present a least-squares weak Galerkin (LS-WG) finite element method for solving the Stokes equations on arbitrary polygonal and polyhedral meshes. By utilizing discrete weak der…
A Least-Squares Weak Galerkin Finite Element Scheme for Cauchy Problems in Helmholtz
Chunmei Wang, Shangyou Zhang
This paper introduces and rigorously analyzes a least-squares weak Galerkin (LS-WG) finite element method for the severely ill-posed Cauchy problem associated with the Helmholtz eq…
A Least-Squares Weak Galerkin Finite Element Scheme for Cauchy Problems in Convection--Diffusion
Chunmei Wang, Shangyou Zhang
We introduce and rigorously analyze a least-squares weak Galerkin (LS-WG) finite element method for the severely ill-posed Cauchy problem of convection--diffusion equations. The pr…
A Least-Squares Weak Galerkin Method for Second-Order Elliptic Equations in Non-Divergence Form
Chunmei Wang, Shangyou Zhang
This article proposes a novel least-squares weak Galerkin (LS-WG) method for second-order elliptic equations in non-divergence form. The approach leverages a locally defined discre…
The finite expression method for turbulent dynamics with high-order moment recovery
Xingjian Xu, Di Qi, Chunmei Wang
Turbulent dynamical systems are characterized by nonlinear interactions and stochastic effects that generate coupled statistical quantities, such as non-zero higher-order moments,…
A Neural-Enhanced Weak Galerkin Method for Second-Order Elliptic Problems with Low-Regularity Solutions
Chunmei Wang
We propose a neural-enhanced weak Galerkin (WG) finite element method for second-order elliptic problems with low-regularity solutions. The method augments the classical WG approxi…
Auto-Stabilized Weak Galerkin Finite Element Methods for Biot's consolidation model on Non-Convex Polytopal Meshes
Chunmei Wang, Shangyou Zhang
This paper presents an auto-stabilized weak Galerkin (WG) finite element method for the Biot's consolidation model within the classical displacement-pressure two-field formulation.…
A Simple Weak Galerkin Finite Element Method for Convection-Diffusion-Reaction Equations on Nonconvex Polytopal Meshes
Chunmei Wang, Shangyou Zhang
This article introduces a simple weak Galerkin (WG) finite element method for solving convection-diffusion-reaction equation. The proposed method offers significant flexibility by…
A weak Galerkin least squares finite element method for linear convection equations in non-divergence form
Chunmei Wang, Shangyou Zhang
This article develops a weak Galerkin least-squares (WG--LS) finite element method for first-order linear convection equations in non-divergence form. The method is formulated usin…