2 citations · 7 across the 9 of their papers we have counts for
8 papers · 1 filter
VPVnet: a velocity-pressure-vorticity neural network method for the Stokes' equations under reduced regularity
Yujie Liu, Chao Yang
We present VPVnet, a deep neural network method for the Stokes' equations under reduced regularity. Different with recently proposed deep learning methods [40,51] which are based o…
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 High order Conservative Flux Optimization Finite Element Method for Diffusion Equations
Yujie Liu, Yue Feng, Ran Zhang
This article presents a high order conservative flux optimization (CFO) finite element method for the elliptic diffusion equations. The numerical scheme is based on the classical G…
A discrete maximum principle for the weak Galerkin finite element method on nonuniform rectangular partitions
Yujie Liu, Junping Wang
This article establishes a discrete maximum principle (DMP) for the approximate solution of convection-diffusion-reaction problems obtained from the weak Galerkin finite element me…
A Simplified Weak Galerkin Finite Element Method: Algorithm and Error Estimates
Yujie Liu, Junping Wang
In this article a simplified weak Galerkin finite element method is developed for the Dirichlet boundary value problem of convection-diffusion-reaction equations. The simplified we…
Simplified Weak Galerkin and New Finite Difference Schemes for the Stokes Equation
Yujie Liu, Junping Wang
This article presents a simplified formulation for the weak Galerkin finite element method for the Stokes equation without using the degrees of freedom associated with the unknowns…
A Conservative Flux Optimization Finite Element Method for Convection-Diffusion Equations
Yujie Liu, Junping Wang, Qingsong Zou
This article presents a new finite element method for convection-diffusion equations by enhancing the continuous finite element space with a flux space for flux approximations that…