Curvature driven surface evolution plays an important role in geometry, applied mathematics
and in the natural sciences. In this paper geometric evolution equations such as mean …

In comparison with the Cahn–Hilliard equation, the classic Allen-Cahn equation satisfies the
maximum bound principle (MBP) but fails to conserve the mass along the time. In this paper …

We consider the numerical approximation of the flow‐coupled phase‐field model of two‐
phase incompressible flows using the mass‐conserved Allen‐Cahn equation. Due to the …

We consider the numerical approximation of the flow-coupled multi-phase-field elastic
bending energy model of lipid vesicles. Based on the classical model with approximate …

In this article, we develop and analyze a novel fully discrete decoupled finite element
method to solve a flow-coupled ternary phase-field model for the system consisting of three …

Compared with the well-known classical Allen–Cahn equation, the modified Allen–Cahn
equation, which is equipped with a nonlocal Lagrange multiplier or a local-nonlocal …

In the present work, we consider the conservative Allen-Cahn model and applied it to two-
phase flows in a consistent and conservative manner. The consistent formulation is …

The main purpose of this paper is to solve the fractional non-local Allen–Cahn model via a
super fast explicit operator splitting spectral (FEOSS) method, which is based on the Strang …

We construct a novel second-order time marching scheme with the full decoupling structure
to solve a highly coupled nonlinear two-phase fluid flow system consisting of the nonlocal …

We present a convergence result for solutions of the vector‐valued Allen‐Cahn equation. In
the spirit of the work of Luckhaus and Sturzenhecker we establish convergence towards a …