Cahn--Hilliard
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Related Articles from SNS
An Energy-Stable Implicit Convex-Splitting BDF2 Scheme for the Cahn-Hilliard-Navier-Stokes Equations
Announce Type: new Abstract: We develop an energy-stable implicit convex-splitting BDF2 discretization (CS-BDF2) of the Cahn--Hilliard--Navier--Stokes equations. For the Cahn--Hilliard equation, BDF2 analyses can establish energy stability by testing the phase equation in the (H^{-1}) metric. For CHNS, this test is not compatible with the coupled energy estimate: the momentum equation is tested by (\bfu^{n+1}), while the transported phase equation is tested by (\mu^{n+1}) so that transport...
Numerical Approximation of the stochastic Cahn--Hilliard equation with singular potential
Announce Type: new Abstract: We discuss the numerical approximation of the stochastic Cahn--Hilliard equation with a singular double-obstacle potential and multiplicative conservative noise. We propose a regularised fully discrete finite element approximation scheme for the problem and show that it satisfies stability estimates which are uniform with respect to the discretization parameters. We show convergence of the approximation for vanishing discretization parameters towards a...
High-order conforming finite elements for the Cahn-Hilliard equation: Relative-energy stability and energy defects
arXiv:2606.06719v1 Announce Type: new Abstract: We study a semidiscrete single-field Galerkin approximation of the Cahn-Hilliard equation using high-order conforming finite element spaces. More specifically, globally $C^1$ finite elements with $H^2$-conforming trial spaces, including Argyris, Bell, and Bogner-Fox-Schmit elements, allow a direct discretization of the fourth-order formulation and preserve mass exactly. The main structural result is an exact energy balance for the physical...
Error estimates for full discretization by an almost mass conservation technique for Cahn--Hilliard systems with dynamic boundary conditions
arXiv:2502.03847v2 Announce Type: replace Abstract: A proof of optimal-order error estimates is given for the full discretization of the bulk--surface Cahn--Hilliard system with dynamic boundary conditions in a smooth domain. The numerical method combines a linear bulk--surface finite element discretization in space and linearly implicit backward difference formulae of order one to five in time. The error estimates are obtained by a consistency and stability analysis, based on an energy...
Justification and structure- and asymptotic-preserving discretizations of a hyperbolized Cahn-Hilliard equation
arXiv:2606.09299v1 Announce Type: new Abstract: We study a hyperbolic approximation ("hyperbolization") of the Cahn-Hilliard (CH) equation, originally proposed by Dhaouadi, Dumbser, and Gavrilyuk (2025, DOI: 10.1098/rspa.2024.0606) and study its convergence towards the CH model in a relaxation limit both via formal asymptotic expansions and, for a slightly modified approximation, via the relative energy framework. Moreover, we develop energy-stable semidiscretizations of the CH equation and...
A simple model for conserved intracellular dynamics exhibits multiscale pattern formation, traveling protein domains and arrested coarsening of lipid domains
Announce Type: replace-cross Abstract: We model the spatiotemporal dynamics of cellular protein concentrations relevant to cell polarity near membranes composed of different lipids. Therefore, we consider a three-variable continuum model for membrane-bound protein, cytosolic protein, and the local composition of a binary lipid membrane. The model contains two globally conserved quantities: the total protein content and the average fractions of the two lipid species.
Neural-Network-based Viscosity Closure for Non-Newtonian Multiphase Flows
arXiv:2605.30659v1 Announce Type: new Abstract: Materials used in polymer-based additive manufacturing processes, such as Digital Light Processing (DLP) and direct ink writing (DIW), typically exhibit non-Newtonian rheology. Carreau--Yasuda and power-law models describe basic shear-thinning and shear-thickening behavior well, but applying them to a new material requires choosing a functional form, deriving it, and re-implementing it inside the flow solver. We present a deployment workflow in...