2 citations · 7 across the 9 of their papers we have counts for
9 papers
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…
Finite element setting for fluid flow simulations with natural enforcement of capillary effects
Julien Bruchon, Yujie Liu, Nicolas Moulin
Capillary phenomena are involved in many industrial processes, especially those dealing with composite manufacturing. However, their modelling is still challenging. Therefore, a fi…
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…