DOI10.1137/S0036142997331669zbMath0947.65109OpenAlexW1975968248MaRDI QIDQ4943622
John W. Barrett, Harald Garcke, James F. Blowey
Publication date: 19 March 2000
Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1137/s0036142997331669
Efficient second-order semi-implicit finite element method for fourth-order nonlinear diffusion equations ⋮
Stability and discretization error analysis for the Cahn–Hilliard system via relative energy estimates ⋮
A multiphase Cahn–Hilliard system with mobilities and the numerical simulation of dewetting ⋮
An active‐set mixed finite element solver for a transient hydrodynamic lubrication problem in the presence of cavitation ⋮
A structure-preserving, upwind-SAV scheme for the degenerate Cahn-Hilliard equation with applications to simulating surface diffusion ⋮
Numerical investigation of the sharp-interface limit of the Navier–Stokes–Cahn–Hilliard equations ⋮
Unconditional Bound-Preserving and Energy-Dissipating Finite-Volume Schemes for the Cahn-Hilliard Equation ⋮
An adaptive time‐stepping scheme for the numerical simulation of Cahn‐Hilliard equation with variable mobility ⋮
A computational framework for the personalized clinical treatment of glioblastoma multiforme ⋮
Structure Preserving Primal Dual Methods for Gradient Flows with Nonlinear Mobility Transport Distances ⋮
A positivity-preserving, energy stable BDF2 scheme with variable steps for the Cahn-Hilliard equation with logarithmic potential ⋮
A linear, second-order, energy stable, fully adaptive finite element method for phase-field modelling of wetting phenomena ⋮
Adaptive discontinuous Galerkin finite element methods for the Allen-Cahn equation on polygonal meshes ⋮
On the Superconvergence of a Hybridizable Discontinuous Galerkin Method for the Cahn–Hilliard Equation ⋮
A nonnegativity preserving scheme for the relaxed Cahn–Hilliard equation with single-well potential and degenerate mobility ⋮
Mass-conservative and positivity preserving second-order semi-implicit methods for high-order parabolic equations ⋮
On efficient second order stabilized semi-implicit schemes for the Cahn-Hilliard phase-field equation ⋮
A numerical method for the Cahn-Hilliard equation with a variable mobility ⋮
An efficient, unconditionally energy stable local discontinuous Galerkin scheme for the Cahn-Hilliard-Brinkman system ⋮
Isogeometric analysis of the Cahn-Hilliard equation -- a convergence study ⋮
Computational studies of coarsening rates for the Cahn-Hilliard equation with phase-dependent diffusion mobility ⋮
A time-adaptive finite volume method for the Cahn-Hilliard and Kuramoto-Sivashinsky equations ⋮
Relaxation of the Cahn–Hilliard equation with singular single-well potential and degenerate mobility ⋮
On the convergence of entropy consistent schemes for lubrication type equations in multiple space dimensions ⋮
On the modelling of biological patterns with mechanochemical models: insights from analysis and computation ⋮
Finite element approximation of a phase field model arising in nanostructure patterning ⋮
Isogeometric analysis of the Cahn-Hilliard phase-field model ⋮
On the use of a diffuse-interface model for the simulation of rigid particles in two-phase Newtonian and viscoelastic fluids ⋮
Fast multilevel solvers for a class of discrete fourth order parabolic problems ⋮
Numerical methods for solving the Cahn-Hilliard equation and its applicability to related energy-based models ⋮
Error analysis of a finite element approximation of a degenerate Cahn-Hilliard equation ⋮
Isogeometric analysis of a phase field model for Darcy flows with discontinuous data ⋮
Fast solution of Cahn-Hilliard variational inequalities using implicit time discretization and finite elements ⋮
An efficient fully-discrete local discontinuous Galerkin method for the Cahn-Hilliard-Hele-Shaw system ⋮
Second order convex splitting schemes for periodic nonlocal Cahn-Hilliard and Allen-Cahn equations ⋮
A second order in time, uniquely solvable, unconditionally stable numerical scheme for Cahn-Hilliard-Navier-Stokes equation ⋮
Hessian informed mirror descent ⋮
Energy Stable Discontinuous Galerkin Finite Element Method for the Allen–Cahn Equation ⋮
Second order schemes and time-step adaptivity for Allen-Cahn and Cahn-Hilliard models ⋮
Energy stable interior penalty discontinuous Galerkin finite element method for Cahn-Hilliard equation ⋮
An efficient two-grid method for the Cahn-Hilliard equation with the concentration-dependent mobility and the logarithmic Flory-Huggins bulk potential ⋮
Phase field computations for surface diffusion and void electromigration in \({\mathbb{R}^3}\) ⋮
An isogeometric finite element formulation for phase transitions on deforming surfaces ⋮
Bound-preserving flux limiting schemes for DG discretizations of conservation laws with applications to the Cahn-Hilliard equation ⋮
Triangulation-based isogeometric analysis of the Cahn-Hilliard phase-field model ⋮
The phase-field transition system with non-homogeneous Cauchy-Stefan-Boltzmann and homogeneous Neumann boundary conditions and non-constant thermal conductivity ⋮
Multi-component chemo-mechanics based on transport relations for the chemical potential ⋮
High order finite element calculations for the Cahn-Hilliard equation ⋮
A two-phase two-fluxes degenerate Cahn-Hilliard model as constrained Wasserstein gradient flow ⋮
Finite element approximation of a three dimensional phase field model for void electromigration ⋮
Isogeometric analysis of the advective Cahn-Hilliard equation: spinodal decomposition under shear flow ⋮
Stable finite element approximation of a Cahn–Hilliard–Stokes system coupled to an electric field ⋮
A parametric finite element method for solid-state dewetting problems with anisotropic surface energies ⋮
Discontinuous Galerkin finite element discretization of a degenerate Cahn-Hilliard equation with a single-well potential ⋮
A phase-field model for liquid-gas mixtures: mathematical modelling and discontinuous Galerkin discretization ⋮
Fast solver of optimal control problems constrained by Ohta-Kawasaki equations ⋮
A fully discrete virtual element scheme for the Cahn-Hilliard equation in mixed form ⋮
An upwind DG scheme preserving the maximum principle for the convective Cahn-Hilliard model ⋮
Multimaterial structural topology optimization with a generalized Cahn-Hilliard model of multiphase transition ⋮
A finite volume/discontinuous Galerkin method for the advective Cahn-Hilliard equation with degenerate mobility on porous domains stemming from micro-CT imaging ⋮
Conservative multigrid methods for Cahn--Hilliard fluids. ⋮
Error control for the approximation of Allen-Cahn and Cahn-Hilliard equations with a logarithmic potential ⋮
FESTUNG 1.0: overview, usage, and example applications of the MATLAB/GNU Octave toolbox for discontinuous Galerkin methods ⋮
Efficient solvers of discontinuous Galerkin discretization for the Cahn-Hilliard equations ⋮
The Cahn-Hilliard equation with logarithmic potentials ⋮
A conservative numerical method for the Cahn-Hilliard equation in complex domains ⋮
Finite element analysis of a nonlinear parabolic equation modeling epitaxial thin-film growth ⋮
On the existence, uniqueness and regularity of solutions to the phase-field system with a general regular potential and a general class of nonlinear and non-homogeneous boundary conditions ⋮
Unconditionally energy stable discontinuous Galerkin schemes for the Cahn-Hilliard equation ⋮
Global solutions to a model with Dirichlet boundary conditions for interface motion by interface diffusion ⋮
An Efficient and Convergent Finite Element Scheme for Cahn--Hilliard Equations with Dynamic Boundary Conditions ⋮
Local discontinuous Galerkin methods for the Cahn-Hilliard type equations ⋮
High-order finite volume methods and multiresolution reproducing kernels ⋮
Error analysis of an unconditionally energy stable local discontinuous Galerkin scheme for the Cahn-Hilliard equation with concentration-dependent mobility ⋮
Finite element approximation of a phase field model for surface diffusion of voids in a stressed solid ⋮
On the stable discretization of strongly anisotropic phase field models with applications to crystal growth ⋮
A fully coupled mixed finite element method for surfactants spreading on thin liquid films ⋮
On a fractional thin film equation ⋮
A discontinuous Galerkin method for the Cahn-Hilliard equation ⋮
Optimal distributed control of nonlinear Cahn-Hilliard systems with computational realization ⋮
Numerical simulation of dealloying by surface dissolution via the evolving surface finite element method ⋮
An adaptive finite element Moreau-Yosida-based solver for a coupled Cahn-Hilliard/Navier-Stokes system ⋮
A non-isothermal compressible Cahn-Hilliard fluid model for air pollution phenomena ⋮
The spectral method for the Cahn-Hilliard equation with concentration-dependent mobility ⋮
A diffuse-interface model for electrowetting drops in a Hele-Shaw cell ⋮
On fully practical finite element approximations of degenerate Cahn-Hilliard systems ⋮
Natural element analysis of the Cahn-Hilliard phase-field model ⋮
A weak Galerkin finite element scheme for the Cahn-Hilliard equation ⋮
Sharp-Interface Limits of the Cahn--Hilliard Equation with Degenerate Mobility ⋮
Asymptotic behaviour of time stepping methods for phase field models ⋮
Regularity of solutions of the Cahn-Hilliard equation with non-constant mobility ⋮
A qualitative analysis of a nonlinear second-order anisotropic diffusion problem with non-homogeneous Cauchy-Stefan-Boltzmann boundary conditions ⋮
Modelling cancer cell budding in-vitro as a self-organised, non-equilibrium growth process ⋮
An adaptive finite-element Moreau–Yosida-based solver for a non-smooth Cahn–Hilliard problem ⋮
A multigrid method for the Cahn-Hilliard equation with obstacle potential ⋮
An energy stable fourth order finite difference scheme for the Cahn-Hilliard equation ⋮
Solving the Cahn-Hilliard variational inequality with a semi-smooth Newton method ⋮
Finite-element approximation of a phase field model for tumour growth ⋮
Equivalence between a time-fractional and an integer-order gradient flow: the memory effect reflected in the energy ⋮
The stochastic Cahn–Hilliard equation with degenerate mobility and logarithmic potential ⋮
A robust and accurate adaptive approximation method for a diffuse-interface model of binary-fluid flows ⋮
Existence of solutions and separation from singularities for a class of fourth order degenerate parabolic equations ⋮
A multilevel Monte Carlo finite element method for the stochastic Cahn-Hilliard-Cook equation ⋮
Nonconforming tetrahedral finite elements for fourth order elliptic equations ⋮
The Cahn-Hilliard equation and some of its variants ⋮
Symmetric interior penalty Galerkin method for fractional-in-space phase-field equations ⋮
Coarsening Mechanism for Systems Governed by the Cahn--Hilliard Equation with Degenerate Diffusion Mobility ⋮
How Do Degenerate Mobilities Determine Singularity Formation in Cahn--Hilliard Equations? ⋮
A multigrid finite element solver for the Cahn-Hilliard equation ⋮
Numerical simulation of a binary alloy of 2D Cahn-Hilliard model for phase separation ⋮
Numerical analysis for a Cahn-Hilliard system modelling tumour growth with chemotaxis and active transport ⋮
Convex Splitting Method for Strongly Anisotropic Solid-State Dewetting Problems in Two Dimensions ⋮
A Second Order Accurate in Time, Energy Stable Finite Element Scheme for the Flory-Huggins-Cahn-Hilliard Equation