We propose a new numerical technique to deal with nonlinear terms in gradient flows. By
introducing a scalar auxiliary variable (SAV), we construct efficient and robust energy stable …

We carry out convergence and error analysis of the scalar auxiliary variable (SAV) methods
for L^2 and H^-1 gradient flows with a typical form of free energy. We first derive H^2 …

The scalar auxiliary variable (SAV) method was introduced by Shen et al. in [36] and has
been broadly used to solve thermodynamically consistent PDE problems. By utilizing scalar …

In this paper we present and analyze finite difference numerical schemes for the Cahn-
Hilliard equation with a logarithmic Flory Huggins energy potential. Both first and second …

In this paper we propose and analyze a second order accurate (in time) numerical scheme
for the square phase field crystal equation, a gradient flow modeling crystal dynamics at the …

In this paper we propose and analyze an energy stable numerical scheme for the Cahn–
Hilliard equation, with second order accuracy in time and the fourth order finite difference …

The scalar auxiliary variable (SAV) approach [31] and its generalized version GSAV
proposed in [20] are very popular methods to construct efficient and accurate energy stable …

In this paper we present a second order accurate (in time) energy stable numerical scheme
for the Cahn-Hilliard (CH) equation, with a mixed finite element approximation in space …

We propose a novel second order in time numerical scheme for Cahn–Hilliard–Navier–
Stokes phase field model with matched density. The scheme is based on second order …

In this paper we propose and analyze a finite difference numerical scheme for the Poisson-
Nernst-Planck equation (PNP) system. To understand the energy structure of the PNP …