The energy dissipation law and the maximum bound principle (MBP) are two important
physical features of the well-known Allen--Cahn equation. While some commonly used first …

We present and analyze a second order in time variable step BDF2 numerical scheme for
the Cahn--Hilliard equation. The construction relies on a second order backward difference …

The maximum bound principle (MBP) is an important property for a large class of semilinear
parabolic equations, in the sense that the time-dependent solution of the equation with …

It is well-known that the Allen–Cahn equation not only satisfies the energy dissipation law
but also possesses the maximum bound principle (MBP) in the sense that the absolute value …

We consider numerical methods for solving the fractional-in-space Allen–Cahn equation
which contains small perturbation parameters and strong nonlinearity. A standard fully …

A large class of semilinear parabolic equations satisfy the maximum bound principle (MBP)
in the sense that the time-dependent solution preserves for any time a uniform pointwise …

We consider several seconder order in time stabilized semi-implicit Fourier spectral
schemes for 2D Cahn–Hilliard equations. We introduce new stabilization techniques and …

Recent results in the literature provide computational evidence that the stabilized semi-
implicit time-step** method can efficiently simulate phase field problems involving fourth …

It is known that the Allen-Chan equations satisfy the maximum principle. Is this true for
numerical schemes? To the best of our knowledge, the state-of-art stability framework is the …

This paper is concerned with the generalized Allen–Cahn equation with a nonlinear mobility
that may be degenerate, which also includes an advection term appearing in many …