10 citations · 29 across the 15 of their papers we have counts for
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A high-order nodally bound-preserving and mass-conservative method for linear fourth-order elliptic problems and its applications to nonlinear parabolic equations
Jie Shen, Zuodong Wang
We propose a high-order finite element method for linear fourth-order elliptic problems that is both nodally bound-preserving and mass-conservative, based on a variational inequali…
A new Lagrange multiplier approach for constructing structure-preserving schemes, II. bound preserving
Qing Cheng, Jie Shen
In the second part of this series, we use the Lagrange multiplier approach proposed in the first part \cite{CheS21} to construct efficient and accurate bound and/or mass preserving…
A fast Petrov-Galerkin spectral method for the multi-dimensional Boltzmann equation using mapped Chebyshev functions
Jingwei Hu, Xiaodong Huang, Jie Shen +1
Numerical approximation of the Boltzmann equation presents a challenging problem due to its high-dimensional, nonlinear, and nonlocal collision operator. Among the deterministic me…
Discrete Maximum principle of a high order finite difference scheme for a generalized Allen-Cahn equation
Jie Shen, Xiangxiong Zhang
We consider solving a generalized Allen-Cahn equation coupled with a passive convection for a given incompressible velocity field. The numerical scheme consists of the first order…
Stability and error analysis of IMEX SAV schemes for the magneto-hydrodynamic equations
Xiaoli Li, Weilong Wang, Jie Shen
We construct and analyze first- and second-order implicit-explicit (IMEX) schemes based on the scalar auxiliary variable (SAV) approach for the magneto-hydrodynamic equations. Thes…
Stability and error analysis of a class of high-order IMEX schemes for Navier-stokes equations with periodic boundary conditions
Fukeng Huang, Jie Shen
We construct high-order semi-discrete-in-time and fully discrete (with Fourier-Galerkin in space) schemes for the incompressible Navier-Stokes equations with periodic boundary cond…