24 papers
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…
Weak Galerkin finite element methods for elliptic interface problems on nonconvex polygonal partitions
Chunmei Wang, Shangyou Zhang
This paper proposes a weak Galerkin (WG) finite element method for elliptic interface problems defined on nonconvex polygonal partitions. The method features a built-in stabilizer…
A Simple Weak Galerkin Finite Element Method for the Reissner-Mindlin Plate Model on Non-Convex Polytopal Meshes
Chunmei Wang, Shangyou Zhang
This paper presents a simple weak Galerkin (WG) finite element method for the Reissner-Mindlin plate model that partially eliminates the need for traditionally employed stabilizers…
A Simple and Robust Weak Galerkin Method for the Brinkman Equations on Non-Convex Polytopal Meshes
Chunmei Wang, Shangyou Zhang
This paper presents a novel Stabilizer-Free weak Galerkin (WG) finite element method for solving the Brinkman equations without the need for conventional stabilization techniques.…
Weak Galerkin Methods for the Brinkman Equations
Chunmei Wang, Shangyou Zhang
This paper introduces a novel weak Galerkin (WG) finite element method for the numerical solution of the Brinkman equations. The Brinkman model, which seamlessly integrates charact…
Stabilizer-free Weak Galerkin Methods for Quad-Curl Problems on polyhedral Meshes without Convexity Assumptions
Chunmei Wang, Shangyou Zhang
This paper introduces an efficient stabilizer-free weak Galerkin (WG) finite element method for solving the three-dimensional quad-curl problem. Leveraging bubble functions as a ke…
An Auto-Stabilized Weak Galerkin Method for Elasticity Interface Problems on Nonconvex Meshes
Chunmei Wang, Shangyou Zhang
This paper introduces an auto-stabilized weak Galerkin (WG) finite element method for elasticity interface problems on general polygonal and polyhedral meshes, without requiring co…
Auto-Stabilized Weak Galerkin Finite Element Methods for Stokes Equations on Non-Convex Polytopal Meshes
Chunmei Wang, Shangyou Zhang
This paper introduces an auto-stabilized weak Galerkin (WG) finite element method for solving Stokes equations without relying on traditional stabilizers. The proposed WG method ac…
Simplified Weak Galerkin Finite Element Methods for Biharmonic Equations on Non-Convex Polytopal Meshes
Chunmei Wang
This paper presents a simplified weak Galerkin (WG) finite element method for solving biharmonic equations avoiding the use of traditional stabilizers. The proposed WG method suppo…
Simplified Weak Galerkin Methods for Linear Elasticity on Nonconvex Domains
Chunmei Wang, Shangyou Zhang
This paper presents a weak Galerkin (WG) finite element method for linear elasticity on general polygonal and polyhedral meshes, free from convexity constraints, by leveraging bubb…
Efficient Weak Galerkin Finite Element Methods for Maxwell Equations on polyhedral Meshes without Convexity Constraints
Chunmei Wang, Shangyou Zhang
This paper presents an efficient weak Galerkin (WG) finite element method with reduced stabilizers for solving the time-harmonic Maxwell equations on both convex and non-convex pol…
Auto-Stabilized Weak Galerkin Finite Element Methods for Biharmonic Equations on Polytopal Meshes without Convexity Assumptions
Chunmei Wang
This paper introduces an auto-stabilized weak Galerkin (WG) finite element method for biharmonic equations with built-in stabilizers. Unlike existing stabilizer-free WG methods lim…
Auto-Stabilized Weak Galerkin Finite Element Methods on Polytopal Meshes without Convexity Constraints
Chunmei Wang
This paper introduces an auto-stabilized weak Galerkin (WG) finite element method with a built-in stabilizer for Poisson equations. By utilizing bubble functions as a key analytica…