Hongxing Rui
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View article: A pressure-robust virtual element method for the Stokes problem
A pressure-robust virtual element method for the Stokes problem Open
We present an arbitrary-order pressure-robust nonconforming virtual element method for the Stokes problem. Based on the local subtriangulations of polygons and the requirement of recovering the orthogonality between the velocity virtual sp…
View article: Robust superconvergence analysis of physics-preserving RMAC scheme for the Stokes and Navier--Stokes equations on non-uniform grids at high Reynolds numbers
Robust superconvergence analysis of physics-preserving RMAC scheme for the Stokes and Navier--Stokes equations on non-uniform grids at high Reynolds numbers Open
The velocity errors of the classical marker and cell (MAC) scheme are dependent on the pressure approximation errors, which is non-pressure-robust and will cause the accuracy of the velocity approximation to deteriorate when the pressure a…
View article: Analysis of a $\boldsymbol{P}_1\oplus \boldsymbol{RT}_0$ finite element method for linear elasticity with Dirichlet and mixed boundary conditions
Analysis of a $\boldsymbol{P}_1\oplus \boldsymbol{RT}_0$ finite element method for linear elasticity with Dirichlet and mixed boundary conditions Open
In this paper, we investigate a low-order robust numerical method for the linear elasticity problem. The method is based on a Bernardi--Raugel-like $\boldsymbol{H}(\mathrm{div})$-conforming method proposed first for the Stokes flows in [Li…
View article: On efficient linear and fully decoupled finite difference method for wormhole propagation with heat transmission process on staggered grids
On efficient linear and fully decoupled finite difference method for wormhole propagation with heat transmission process on staggered grids Open
In this paper, we construct an efficient linear and fully decoupled finite difference scheme for wormhole propagation with heat transmission process on staggered grids, which only requires solving a sequence of linear elliptic equations at…
View article: An EMA-conserving, pressure-robust and Re-semi-robust method with A robust reconstruction method for Navier–Stokes
An EMA-conserving, pressure-robust and Re-semi-robust method with A robust reconstruction method for Navier–Stokes Open
Proper EMA-balance (balance of kinetic energy, linear momentum and angular momentum), pressure-robustness and Re-semi-robustness ( Re : Reynolds number) are three important properties of Navier–Stokes simulations with exactly divergence-fr…
View article: Inf-sup stabilized Scott--Vogelius pairs on general simplicial grids by Raviart--Thomas enrichment
Inf-sup stabilized Scott--Vogelius pairs on general simplicial grids by Raviart--Thomas enrichment Open
This paper considers the discretization of the Stokes equations with Scott--Vogelius pairs of finite element spaces on arbitrary shape-regular simplicial grids. A novel way of stabilizing these pairs with respect to the discrete inf-sup co…
View article: Longer time simulation of the unsteady Navier-Stokes equations based on a modified convective formulation
Longer time simulation of the unsteady Navier-Stokes equations based on a modified convective formulation Open
For the discretization of the convective term in the Navier-Stokes equations (NSEs), the commonly used convective formulation (CONV) does not preserve the energy if the divergence constraint is only weakly enforced. In this paper, we apply…
View article: An EMA-balancing, pressure-robust and Re-semi-robust reconstruction method for unsteady incompressible Navier-Stokes equations
An EMA-balancing, pressure-robust and Re-semi-robust reconstruction method for unsteady incompressible Navier-Stokes equations Open
Proper EMA-balance (E: kinetic energy; M: momentum; A: angular momentum), pressure-robustness and $Re$-semi-robustness ($Re$: Reynolds number) are three important properties for exactly divergence-free elements in Navier-Stokes simulations…
View article: An EMA-conserving, pressure-robust and Re-semi-robust reconstruction method for the unsteady incompressible Navier-Stokes equations
An EMA-conserving, pressure-robust and Re-semi-robust reconstruction method for the unsteady incompressible Navier-Stokes equations Open
Proper EMA-balance (E: kinetic energy; M: momentum; A: angular momentum), pressure-robustness and $Re$-semi-robustness ($Re$: Reynolds number) are three important properties of Navier-Stokes simulations with exactly divergence-free element…
View article: New Energy Analysis of Yee Scheme for Metamaterial Maxwell's Equations on Non-Uniform Rectangular Meshes
New Energy Analysis of Yee Scheme for Metamaterial Maxwell's Equations on Non-Uniform Rectangular Meshes Open
In this paper, several new energy identities of metamaterial Maxwell's equations with the perfectly electric conducting (PEC) boundary condition are proposed and proved.These new energy identities are different from the Poynting theorem.By…
View article: A compact divergence-free H(div)-conforming finite element method for Stokes flows
A compact divergence-free H(div)-conforming finite element method for Stokes flows Open
In this paper, we construct a $P_{1}^{c}\oplus RT0-P0$ discretization of the Stokes equations for general simplicial meshes in two/three dimensions (2D/3D), which yields a exactly divergence-free and pressure-independent velocity approxima…
View article: A low order divergence-free H(div)-conforming finite element method for Stokes flows
A low order divergence-free H(div)-conforming finite element method for Stokes flows Open
In this paper, we propose a ${ P_{1}^{c}}\oplus {RT0}-P0$ discretization of the Stokes equations on general simplicial meshes in two/three dimensions (2D/3D), which yields an exactly divergence-free and pressure-independent velocity approx…
View article: A Stabilized Hybrid Mixed Finite Element Method for Poroelasticity
A Stabilized Hybrid Mixed Finite Element Method for Poroelasticity Open
In this work, we consider a hybrid mixed finite element method for Biot's model. The hybrid P1-RT0-P0 discretization of the displacement-pressure-Darcy's velocity system of Biot's model presented in \cite{C. Niu} is not uniformly stable wi…
View article: Energy stability and convergence of SAV block-centered finite difference method for gradient flows
Energy stability and convergence of SAV block-centered finite difference method for gradient flows Open
We present in this paper construction and analysis of a block-centered finite difference method for the spatial discretization of the scalar auxiliary variable Crank-Nicolson scheme (SAV/CN-BCFD) for gradient flows, and show rigorously tha…
View article: Energy Stability and Convergence of SAV Block-centered Finite Difference Method for Gradient Flows
Energy Stability and Convergence of SAV Block-centered Finite Difference Method for Gradient Flows Open
We present in this paper construction and analysis of a block-centered finite difference method for the spatial discretization of the scalar auxiliary variable Crank-Nicolson scheme (SAV/CN-BCFD) for gradient flows, and show rigorously tha…
View article: Multigrid Methods for A Mixed Finite Element Method of The Darcy-Forchheimer Model
Multigrid Methods for A Mixed Finite Element Method of The Darcy-Forchheimer Model Open
An efficient nonlinear multigrid method for a mixed finite element method of the Darcy-Forchheimer model is constructed in this paper. A Peaceman-Rachford type iteration is used as a smoother to decouple the nonlinearity from the divergenc…