We introduce provably unconditionally stable mixed variational methods for phase-field
models. Our formulation is based on a mixed finite element method for space discretization …

We present an efficient numerical framework for analyzing spinodal decomposition
described by the Cahn–Hilliard equation. We focus on the analysis of various implicit time …

Phase-field modeling is emerging as a promising tool for the treatment of problems with
interfaces. The classical description of interface problems requires the numerical solution of …

We consider the numerical approximation of high order Partial Differential Equations (PDEs)
defined on surfaces in the three dimensional space, with particular emphasis on closed …

We present a numerical study of the spinodal decomposition of a binary fluid undergoing
shear flow using the advective Cahn–Hilliard equation, a stiff, nonlinear, parabolic equation …

We present a phase field model of infiltration that explains the formation of gravity fingers
during water infiltration in soil. The model is an extension of the traditional Richards …

Abstract We propose a Convex Splitting Runge–Kutta (CSRK) scheme which provides a
simple unified framework to solve a gradient flow in an unconditionally gradient stable …

In this work, a Cahn–Hilliard phase-field model coupled with mechanics is proposed and
implemented with the isogeometric finite element method in 3D. Thereby, phase-dependent …

In this paper, a fractional extension of the Cahn–Hilliard (CH) phase field model is proposed,
ie the fractional-in-space CH equation. The fractional order controls the thickness and the …

Lithium-ion batteries exhibit complex nonlinear dynamics, resulting from diffusion and phase
transformations coupled to ion-intercalation reactions. Using the recently developed Cahn …