365 citations · 921 across the 25 of their papers we have counts for
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On fully decoupled MSAV schemes for the Cahn-Hilliard-Navier-Stokes model of Two-Phase Incompressible Flows
Xiaoli Li, Jie Shen
We construct first- and second-order time discretization schemes for the Cahn-Hilliard-Navier-Stokes system based on the multiple scalar auxiliary variables approach (MSAV) approac…
Unconditionally positivity preserving and energy dissipative schemes for Poisson--Nernst--Planck equations
Jie Shen, Jie Xu
We develop a set of numerical schemes for the Poisson--Nernst--Planck equations. We prove that our schemes are mass conservative, uniquely solvable and keep positivity unconditiona…
Efficient Linear and Unconditionally Energy Stable Schemes for the Modified Phase Field Crystal Equation
Xiaoli Li, Jie Shen
In this paper, we construct efficient schemes based on the scalar auxiliary variable (SAV) block-centered finite difference method for the modified phase field crystal (MPFC) equat…
Log orthogonal functions: approximation properties and applications
Sheng Chen, Jie Shen
We present two new classes of orthogonal functions, log orthogonal functions (LOFs) and generalized log orthogonal functions (GLOFs), which are constructed by applying a map…
New SAV-pressure correction methods for the Navier-Stokes equations: stability and error analysis
Xiaoli Li, Jie Shen, Zhengguang Liu
We construct new first- and second-order pressure correction schemes using the scalar auxiliary variable (SAV) approach for the Navier-Stokes equations. These schemes are linear, d…