A new class of implicit–explicit BDFk SAV schemes for general dissipative systems and their error analysis

A Second Order Accurate Scalar Auxiliary Variable (SAV) Numerical Method for the Square Phase Field Crystal Equation

(2021) Min Wang et al.   JOURNAL OF SCIENTIFIC COMPUTING

The BDF3/EP3 Scheme for MBE with No Slope Selection is Stable

(2021) Dong Li et al.   JOURNAL OF SCIENTIFIC COMPUTING

Stability and error estimates of the SAV Fourier-spectral method for the phase field crystal equation

(2020) Xiaoli Li et al.   ADVANCES IN COMPUTATIONAL MATHEMATICS

Optimal error estimates for the scalar auxiliary variable finite-element schemes for gradient flows

(2020) Hongtao Chen et al.   NUMERISCHE MATHEMATIK

Linearly Implicit and High-Order Energy-Conserving Schemes for Nonlinear Wave Equations

(2020) Dongfang Li et al.   JOURNAL OF SCIENTIFIC COMPUTING

gPAV-based unconditionally energy-stable schemes for the Cahn–Hilliard equation: Stability and error analysis

(2020) Yanxia Qian et al.   COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING

Energy stability and convergence of SAV block-centered finite difference method for gradient flows

(2019) Xiaoli Li et al.   MATHEMATICS OF COMPUTATION

The scalar auxiliary variable (SAV) approach for gradient flows

(2018) Jie Shen et al.   JOURNAL OF COMPUTATIONAL PHYSICS

Convergence and Error Analysis for the Scalar Auxiliary Variable (SAV) Schemes to Gradient Flows

(2018) Jie Shen et al.   SIAM JOURNAL ON NUMERICAL ANALYSIS

Characterizing the Stabilization Size for Semi-Implicit Fourier-Spectral Method to Phase Field Equations

(2016) Dong Li et al.   SIAM JOURNAL ON NUMERICAL ANALYSIS

Stability of Implicit-Explicit Backward Difference Formulas For Nonlinear Parabolic Equations

(2015) Georgios Akrivis   SIAM JOURNAL ON NUMERICAL ANALYSIS

Numerical approximations of Allen-Cahn and Cahn-Hilliard equations

(2010) Jie Shen et al.   DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS

Spectral approximation of pattern-forming nonlinear evolution equations with double-well potentials of quadratic growth

(2010) Nicolas Condette et al.   MATHEMATICS OF COMPUTATION