In this paper we propose and analyze a (temporally) third order accurate exponential time
differencing (ETD) numerical scheme for the no-slope-selection (NSS) equation of the …

Although the stabilization technique is favorable in designing unconditionally energy stable
or maximum-principle-preserving schemes for gradient flow systems, the induced time delay …

Stabilization techniques are frequently used to construct efficient and stable schemes for stiff
and nonlinear systems. However, the introduced errors may lead to severe delay effects …

Two-phase systems with surfactants have extensive applications in scientific and industrial
fields. In this paper, we consider a second-order time-accurate, highly efficient, and energy …

Abstract The Rayleigh–Plateau instability is a typical multi-phase fluid interface problem
which is driven by the surface tension. After the break-up of a liquid thread, the satellites …

We present an unconditionally stable splitting method for the Allen–Cahn (AC) equation with
logarithmic free energy which is more physically meaningful than the commonly used …

In this paper, we propose several novel recovery based finite element methods for the 2D
Cahn-Hilliard equation. One distinguishing feature of those methods is that we discretize the …

An effective time step analysis to the linear convex splitting scheme for the Allen–Cahn
equation with a high‐order polynomial free energy is presented in this article. Although the …

In this paper, we construct and analyze an energy stable scheme by combining the latest
developed scalar auxiliary variable (SAV) approach and linear finite element method (FEM) …

We propose an unconditionally gradient stable scheme for solving the Cahn–Hilliard
equation with second‐order accuracy in time using the effective time‐step analysis. The …