DOI10.1137/0728069zbMath0744.65089OpenAlexW1992445851MaRDI QIDQ3982650
R. A. Nicolaides, Qiang Du
Publication date: 26 June 1992
Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)
Full work available at URL: https://semanticscholar.org/paper/c407eb05323f4440589b253c8a1bb1803bf506fc
A two-level finite element method for the Allen–Cahn equation ⋮
Fully-discrete finite element numerical scheme with decoupling structure and energy stability for the Cahn–Hilliard phase-field model of two-phase incompressible flow system with variable density and viscosity ⋮
On the Superconvergence of a Hybridizable Discontinuous Galerkin Method for the Cahn–Hilliard Equation ⋮
A Stable Arbitrarily High Order Time-Stepping Method for Thermal Phase Change Problems ⋮
Energy stable and large time-stepping methods for the Cahn–Hilliard equation ⋮
Unconditional convergence analysis of stabilized FEM-SAV method for Cahn-Hilliard equation ⋮
A Second-Order Accurate, Operator Splitting Scheme for Reaction-Diffusion Systems in an Energetic Variational Formulation ⋮
An entropy stable scheme for the non-linear Boltzmann equation ⋮
Generalized SAV-Exponential Integrator Schemes for Allen--Cahn Type Gradient Flows ⋮
On the Cahn-Hilliard equation with no-flux and strong anchoring conditions ⋮
Efficient second-order semi-implicit finite element method for fourth-order nonlinear diffusion equations ⋮
Gradient Flows for Coupling Order Parameters and Mechanics ⋮
Stability and discretization error analysis for the Cahn–Hilliard system via relative energy estimates ⋮
Diagonalization based parallel-in-time method for a class of fourth order time dependent PDEs ⋮
Up to eighth-order maximum-principle-preserving methods for the Allen-Cahn equation ⋮
High-order supplementary variable methods for thermodynamically consistent partial differential equations ⋮
A weak Galerkin finite element method for Allen–Cahn equation with a nonuniform two‐step backward differentiation formula scheme ⋮
A structure-preserving, upwind-SAV scheme for the degenerate Cahn-Hilliard equation with applications to simulating surface diffusion ⋮
On a novel fully-decoupled, linear and second-order accurate numerical scheme for the Cahn-Hilliard-Darcy system of two-phase Hele-Shaw flow ⋮
The convergence of attractors for some discrete Cahn-Hilliard systems ⋮
Analysis of the Morley element for the Cahn–Hilliard equation and the Hele-Shaw flow ⋮
Double stabilizations and convergence analysis of a second-order linear numerical scheme for the nonlocal Cahn-Hilliard equation ⋮
An extended quadratic auxiliary variable method for the singular Lennard-Jones droplet liquid film model ⋮
Positivity-preserving, energy stable numerical schemes for the Cahn-Hilliard equation with logarithmic potential ⋮
Lack of robustness and accuracy of many numerical schemes for phase-field simulations ⋮
Dissipation-preserving discretization of the Cahn-Hilliard equation with dynamic boundary conditions ⋮
An adaptive discontinuous finite volume element method for the Allen-Cahn equation ⋮
Recovery type a posteriori error estimation of an adaptive finite element method for Cahn-Hilliard equation ⋮
Linear and nonlinear Dirichlet–Neumann methods in multiple subdomains for the Cahn–Hilliard equation ⋮
The subdivision-based IGA-EIEQ numerical scheme for the Cahn-Hilliard-Darcy system of two-phase Hele-Shaw flow on complex curved surfaces ⋮
A fully discrete virtual element scheme for the Cahn-Hilliard equation in mixed form ⋮
Convergence of substructuring methods for the Cahn-Hilliard equation ⋮
Minimizers for the Cahn--Hilliard Energy Functional under Strong Anchoring Conditions ⋮
A Second Order BDF Numerical Scheme with Variable Steps for the Cahn--Hilliard Equation ⋮
Energy stability and error estimates of exponential time differencing schemes for the epitaxial growth model without slope selection ⋮
Thermodynamically consistent phase-field modelling of contact angle hysteresis ⋮
A discontinuous Galerkin method for the Cahn-Hilliard equation ⋮
Stabilized Crank-Nicolson/Adams-Bashforth Schemes for Phase Field Models ⋮
A Second-Order Energy Stable BDF Numerical Scheme for the Cahn-Hilliard Equation ⋮
High Accuracy Benchmark Problems for Allen-Cahn and Cahn-Hilliard Dynamics ⋮
An Energy Stable BDF2 Fourier Pseudo-Spectral Numerical Scheme for the Square Phase Field Crystal Equation ⋮
Convergence Analysis of Exponential Time Differencing Schemes for the Cahn-Hilliard Equation<sup>†</sup> ⋮
Error estimates for approximations of a gradient dynamics for phase field elastic bending energy of vesicle membrane deformation ⋮
A Time Splitting Space Spectral Element Method for the Cahn-Hilliard Equation ⋮
Asymptotically Compatible Fourier Spectral Approximations of Nonlocal Allen--Cahn Equations ⋮
Convergence and Error Analysis for the Scalar Auxiliary Variable (SAV) Schemes to Gradient Flows ⋮
Stabilized semi-implicit spectral deferred correction methods for Allen-Cahn and Cahn-Hilliard equations ⋮
Error Estimates with Smooth and Nonsmooth Data for a Finite Element Method for the Cahn-Hilliard Equation ⋮
Analysis of Mixed Interior Penalty Discontinuous Galerkin Methods for the Cahn–Hilliard Equation and the Hele–Shaw Flow ⋮
On Energy Dissipation Theory and Numerical Stability for Time-Fractional Phase-Field Equations ⋮
Spectral approximation of pattern-forming nonlinear evolution equations with double-well potentials of quadratic growth ⋮
Convergence analysis of a fully discrete finite difference scheme for the Cahn-Hilliard-Hele-Shaw equation ⋮
A Hybrid High-Order Method for the Cahn--Hilliard problem in Mixed Form ⋮
Stability and convergence of second-order schemes for the nonlinear epitaxial growth model without slope selection ⋮
On a Novel Fully Decoupled, Second-Order Accurate Energy Stable Numerical Scheme for a Binary Fluid-Surfactant Phase-Field Model ⋮
The IEQ and SAV approaches and their extensions for a class of highly nonlinear gradient flow systems ⋮
Nonconforming tetrahedral finite elements for fourth order elliptic equations ⋮
FINITE ELEMENT METHOD FOR A NONLINEAR DIFFERENTIAL EQUATION DESCRIBING CRYSTAL SURFACE GROWTH ⋮
Fully discrete dynamic mesh discontinuous Galerkin methods for the Cahn-Hilliard equation of phase transition ⋮
Error estimates of fully discrete finite element solutions for the 2D Cahn–Hilliard equation with infinite time horizon ⋮
Uniform \(H^{2}\)-regularity of solution for the 2D Navier-Stokes/Cahn-Hilliard phase field model ⋮
A class of stable and conservative finite difference schemes for the Cahn-Hilliard equation ⋮
Stabilized semi-implicit numerical schemes for the Cahn-Hilliard-like equation with variable interfacial parameter ⋮
Some energy preserving finite element schemes based on the discrete variational derivative method ⋮
High order, semi-implicit, energy stable schemes for gradient flows ⋮
A second-order time accurate and fully-decoupled numerical scheme of the Darcy-Newtonian-nematic model for two-phase complex fluids confined in the Hele-Shaw cell ⋮
Stabilized finite element methods based on multiscale enrichment for Allen-Cahn and Cahn-Hilliard equations ⋮
On efficient second order stabilized semi-implicit schemes for the Cahn-Hilliard phase-field equation ⋮
Computational studies of coarsening rates for the Cahn-Hilliard equation with phase-dependent diffusion mobility ⋮
Efficient numerical solution of discrete multi-component Cahn-Hilliard systems ⋮
A positivity preserving and conservative variational scheme for phase-field modeling of two-phase flows ⋮
A nonstiff, adaptive mesh refinement-based method for the Cahn-Hilliard equation ⋮
On uniform in time \(H^2\)-regularity of the solution for the 2D Cahn-Hilliard equation ⋮
Isogeometric analysis of the Cahn-Hilliard phase-field model ⋮
A nonconforming finite element method for the Cahn-Hilliard equation ⋮
Unconditionally energy stable and bound-preserving schemes for phase-field surfactant model with moving contact lines ⋮
Fast multilevel solvers for a class of discrete fourth order parabolic problems ⋮
An unconditionally energy-stable method for the phase field crystal equation ⋮
Numerical methods for solving the Cahn-Hilliard equation and its applicability to related energy-based models ⋮
Energy stable and efficient finite-difference nonlinear multigrid schemes for the modified phase field crystal equation ⋮
High accuracy solutions to energy gradient flows from material science models ⋮
Accurate, efficient, and (iso)geometrically flexible collocation methods for phase-field models ⋮
Second order schemes and time-step adaptivity for Allen-Cahn and Cahn-Hilliard models ⋮
A second-order, weakly energy-stable pseudo-spectral scheme for the Cahn-Hilliard equation and its solution by the homogeneous linear iteration method ⋮
Unconditionally energy stable second-order numerical scheme for the Allen-Cahn equation with a high-order polynomial free energy ⋮
Finite element methods for one dimensional fourth order semilinear partial differential equation ⋮
An energy stable linear diffusive Crank-Nicolson scheme for the Cahn-Hilliard gradient flow ⋮
Unconditionally energy stable large time stepping method for the \(L^2\)-gradient flow based ternary phase-field model with precise nonlocal volume conservation ⋮
A parallel finite element method for 3D two-phase moving contact line problems in complex domains ⋮
A B-spline finite element method for nonlinear differential equations describing crystal surface growth with variable coefficient ⋮
Optimal error estimates for the scalar auxiliary variable finite-element schemes for gradient flows ⋮
Nonlinear Galerkin finite element methods for fourth-order bi-flux diffusion model with nonlinear reaction term ⋮
Structure-preserving numerical approximations to a non-isothermal hydrodynamic model of binary fluid flows ⋮
A stable, convergent, conservative and linear finite difference scheme for the Cahn-Hilliard equation ⋮
An unconditionally energy stable second order finite element method for solving the Allen-Cahn equation ⋮
Multiphase Allen-Cahn and Cahn-Hilliard models and their discretizations with the effect of pairwise surface tensions ⋮
Multiscale model reduction for the Allen-Cahn problem in perforated domains ⋮
A gradient stable scheme for a phase field model for the moving contact line problem ⋮
A three level linearized compact difference scheme for the Cahn-Hilliard equation ⋮
Bracket formulations and energy- and helicity-preserving numerical methods for incompressible two-phase flows
This page was built for publication: Numerical Analysis of a Continuum Model of Phase Transition