DOI10.1137/090752675zbMath1230.82005OpenAlexW2521393946MaRDI QIDQ3097440
Cheng Wang, Steven M. Wise
Publication date: 10 November 2011
Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)
Full work available at URL: https://semanticscholar.org/paper/3e989e0d2fbc2aa8803ca650fa6d8cdf74414f38
A Stable Arbitrarily High Order Time-Stepping Method for Thermal Phase Change Problems ⋮
Unconditional Superconvergence Analysis of Energy Conserving Finite Element Methods for the Nonlinear Coupled Klein-Gordon Equations ⋮
Fourth-Order Structure-Preserving Method for the Conservative Allen-Cahn Equation ⋮
The numerical simulation of the phase field crystal (PFC) and modified phase field crystal (MPFC) models via global and local meshless methods ⋮
A C0 interior penalty method for mth-Laplace equation ⋮
Phase-field crystal equation with memory ⋮
Numerical Approximations of Phase Field Models Using a General Class of Linear Time-Integration Schemes ⋮
A Modified Crank-Nicolson Numerical Scheme for the Flory-Huggins Cahn-Hilliard Model ⋮
Unnamed Item ⋮
Nonconforming finite element spaces for $2m$th order partial differential equations on $\mathbb {R}^n$ simplicial grids when $m=n+1$ ⋮
Sixth-order Cahn–Hilliard equations with singular nonlinear terms ⋮
A second-order, weakly energy-stable pseudo-spectral scheme for the Cahn-Hilliard equation and its solution by the homogeneous linear iteration method ⋮
Efficient Second Order Unconditionally Stable Schemes for a Phase Field Moving Contact Line Model Using an Invariant Energy Quadratization Approach ⋮
Well-posedness and long-time behavior for the modified phase-field crystal equation ⋮
Error estimates for the scalar auxiliary variable (SAV) schemes to the viscous Cahn-Hilliard equation with hyperbolic relaxation ⋮
Discovering phase field models from image data with the pseudo-spectral physics informed neural networks ⋮
New efficient time-stepping schemes for the anisotropic phase-field dendritic crystal growth model ⋮
Energy stable multigrid method for local and non-local hydrodynamic models for freezing ⋮
Higher-order anisotropic models in phase separation ⋮
Optimized Schwarz Methods for the Cahn–Hilliard Equation ⋮
Efficient unconditionally stable numerical schemes for a modified phase field crystal model with a strong nonlinear vacancy potential ⋮
A linear adaptive second‐order backward differentiation formulation scheme for the phase field crystal equation ⋮
A positivity-preserving and convergent numerical scheme for the binary fluid-surfactant system ⋮
A second order accurate, positivity preserving numerical method for the Poisson-Nernst-Planck system and its convergence analysis ⋮
Spectral deferred correction method for Landau-Brazovskii model with convex splitting technique ⋮
Optimal error estimates of a time-splitting Fourier pseudo-spectral scheme for the Klein-Gordon-Dirac equation ⋮
Unconditional energy stability and temporal convergence of first-order numerical scheme for the square phase-field crystal model ⋮
An efficient and robust Lagrange multiplier approach with a penalty term for phase-field models ⋮
A uniquely solvable, positivity-preserving and unconditionally energy stable numerical scheme for the functionalized Cahn-Hilliard equation with logarithmic potential ⋮
Highly efficient, decoupled and unconditionally stable numerical schemes for a modified phase-field crystal model with a strong nonlinear vacancy potential ⋮
A deep learning method for the dynamics of classic and conservative Allen-Cahn equations based on fully-discrete operators ⋮
Numerical analysis of a second-order energy-stable finite element method for the Swift-Hohenberg equation ⋮
Nonconforming mixed finite element method for the diffuse interface model of two-phase fluid flows ⋮
A second-order exponential time differencing multi-step energy stable scheme for Swift-Hohenberg equation with quadratic-cubic nonlinear term ⋮
Low regularity integrators for semilinear parabolic equations with maximum bound principles ⋮
An energy-stable second-order finite element method for the Swift-Hohenberg equation ⋮
Stability and error estimates of GPAV-based unconditionally energy-stable scheme for phase field crystal equation ⋮
Positivity-preserving, energy stable numerical schemes for the Cahn-Hilliard equation with logarithmic potential ⋮
Unconditionally energy-stable linear convex splitting algorithm for the \(L^2\) quasicrystals ⋮
Phase-field simulation of multiple fluid vesicles with a consistently energy-stable implicit-explicit method ⋮
A Second-Order, Linear, \(\boldsymbol{L^\infty}\)-Convergent, and Energy Stable Scheme for the Phase Field Crystal Equation ⋮
A highly efficient and accurate new SAV approach for the modified phase field crystal model ⋮
Efficient linear schemes for the nonlocal Cahn-Hilliard equation of phase field models ⋮
The Exponential Scalar Auxiliary Variable (E-SAV) Approach for Phase Field Models and Its Explicit Computing ⋮
A BDF2 energy‐stable scheme for the binary fluid‐surfactant hydrodynamic model ⋮
Error analysis of second-order IEQ numerical schemes for the viscous Cahn-Hilliard equation with hyperbolic relaxation ⋮
Generalized Allen-Cahn-type phase-field crystal model with FCC ordering structure and its conservative high-order accurate algorithm ⋮
Convergence of a Fast Explicit Operator Splitting Method for the Epitaxial Growth Model with Slope Selection ⋮
Numerical approximations for a three-component Cahn–Hilliard phase-field model based on the invariant energy quadratization method ⋮
Some discrete inequalities for central-difference type operators ⋮
Numerical approximations for a new \(L^2\)-gradient flow based phase field crystal model with precise nonlocal mass conservation ⋮
Efficient second order unconditionally stable time marching numerical scheme for a modified phase-field crystal model with a strong nonlinear vacancy potential ⋮
A fully discrete virtual element scheme for the Cahn-Hilliard equation in mixed form ⋮
Arbitrarily high-order unconditionally energy stable SAV schemes for gradient flow models ⋮
An upwind DG scheme preserving the maximum principle for the convective Cahn-Hilliard model ⋮
Asymptotic behavior of a sixth-order Cahn-Hilliard system ⋮
Higher-Order Allen–Cahn Models with Logarithmic Nonlinear Terms ⋮
Unnamed Item ⋮
Energy stability and convergence of SAV block-centered finite difference method for gradient flows ⋮
A Second Order BDF Numerical Scheme with Variable Steps for the Cahn--Hilliard Equation ⋮
An efficient finite difference scheme for the 2D sine-Gordon equation ⋮
Unnamed Item ⋮
Efficient Numerical Methods for Computing the Stationary States of Phase Field Crystal Models ⋮
A Convex-Splitting Scheme for a Diffuse Interface Model with Peng-Robinson Equation of State ⋮
A Second-Order Energy Stable BDF Numerical Scheme for the Cahn-Hilliard Equation ⋮
Optimal Convergence Analysis of a Mixed Finite Element Method for Fourth-Order Elliptic Problems ⋮
A High Order Adaptive Time-Stepping Strategy and Local Discontinuous Galerkin Method for the Modified Phase Field Crystal Equation ⋮
Linear and Unconditionally Energy Stable Schemes for the Multi-Component Two-Phase Diffuse Interface Model with Peng-Robinson Equation of State ⋮
An Energy Stable BDF2 Fourier Pseudo-Spectral Numerical Scheme for the Square Phase Field Crystal Equation ⋮
A Positivity-Preserving Second-Order BDF Scheme for the Cahn-Hilliard Equation with Variable Interfacial Parameters ⋮
Fully Decoupled, Linear and Unconditionally Energy Stable Schemes for the Binary Fluid-Surfactant Model ⋮
A <scp>Fourier</scp> pseudospectral method for the “good” <scp>Boussinesq</scp> equation with second‐order temporal accuracy ⋮
Energy-Decaying Extrapolated RK--SAV Methods for the Allen--Cahn and Cahn--Hilliard Equations ⋮
Decoupled energy stable schemes for a phase-field model of two-phase incompressible flows with variable density ⋮
Arbitrarily High-Order Unconditionally Energy Stable Schemes for Thermodynamically Consistent Gradient Flow Models ⋮
Convergence analysis of a fully discrete finite difference scheme for the Cahn-Hilliard-Hele-Shaw equation ⋮
On a SAV-MAC scheme for the Cahn–Hilliard–Navier–Stokes phase-field model and its error analysis for the corresponding Cahn–Hilliard–Stokes case ⋮
First- and second-order energy stable methods for the modified phase field crystal equation ⋮
A second order numerical scheme for the annealing of metal-intermetallic laminate composite: a ternary reaction system ⋮
Energy Stable Numerical Schemes for a Hydrodynamic Model of Nematic Liquid Crystals ⋮
Energy stable and convergent finite element schemes for the modified phase field crystal equation ⋮
An energy stable fourth order finite difference scheme for the Cahn-Hilliard equation ⋮
Structure-Preserving, Energy Stable Numerical Schemes for a Liquid Thin Film Coarsening Model ⋮
A positivity-preserving, energy stable and convergent numerical scheme for the Poisson-Nernst-Planck system ⋮
Sixth-order Cahn-Hilliard systems with dynamic boundary conditions ⋮
Energy stable semi-implicit schemes for Allen-Cahn-Ohta-Kawasaki model in binary system ⋮
The Cahn-Hilliard equation and some of its variants ⋮
Decoupled, Linear, and Unconditionally Energy Stable Fully Discrete Finite Element Numerical Scheme for a Two-Phase Ferrohydrodynamics Model ⋮
Adaptive Second-Order Crank--Nicolson Time-Stepping Schemes for Time-Fractional Molecular Beam Epitaxial Growth Models ⋮
Time Stability of Strong Boundary Conditions in Finite-Difference Schemes for Hyperbolic Systems ⋮
The convergence of two linearized finite difference schemes for the modified phase field crystal equation ⋮
Error estimates of fully discrete finite element solutions for the 2D Cahn–Hilliard equation with infinite time horizon ⋮
Numerical approximations for a phase field dendritic crystal growth model based on the invariant energy quadratization approach ⋮
Numerical analysis of second order, fully discrete energy stable schemes for phase field models of two-phase incompressible flows ⋮
A novel second-order time accurate fully discrete finite element scheme with decoupling structure for the hydrodynamically-coupled phase field crystal model ⋮
A novel second-order linear scheme for the Cahn-Hilliard-Navier-Stokes equations ⋮
A linearly second-order, unconditionally energy stable scheme and its error estimates for the modified phase field crystal equation ⋮
A positive and energy stable numerical scheme for the Poisson-Nernst-Planck-Cahn-Hilliard equations with steric interactions ⋮
A positivity-preserving, energy stable scheme for a ternary Cahn-Hilliard system with the singular interfacial parameters ⋮
Second order linear decoupled energy dissipation rate preserving schemes for the Cahn-Hilliard-extended-Darcy model ⋮
Stable and efficient finite-difference nonlinear-multigrid schemes for the phase field crystal equation ⋮
Unconditionally stable numerical methods for Cahn-Hilliard-Navier-Stokes-Darcy system with different densities and viscosities ⋮
Improving the accuracy and consistency of the scalar auxiliary variable (SAV) method with relaxation ⋮
Fully discrete spectral-Galerkin linear and unconditionally energy stable algorithm for the square phase-field crystal system ⋮
Unconditionally energy stable linear schemes for the diffuse interface model with Peng-Robinson equation of state ⋮
A stabilized fully-discrete scheme for phase field crystal equation ⋮
Linear, second order and unconditionally energy stable schemes for the viscous Cahn-Hilliard equation with hyperbolic relaxation using the invariant energy quadratization method ⋮
Semi-discrete energy-stable schemes for a tensor-based hydrodynamic model of nematic liquid crystal flows ⋮
An unconditionally energy-stable method for the phase field crystal equation ⋮
Energy stable and efficient finite-difference nonlinear multigrid schemes for the modified phase field crystal equation ⋮
Optimal rate convergence analysis of a numerical scheme for the ternary Cahn-Hilliard system with a Flory-Huggins-deGennes energy potential ⋮
Numerical approximations of flow coupled binary phase field crystal system: fully discrete finite element scheme with second-order temporal accuracy and decoupling structure ⋮
A linear unconditionally stable scheme for the incompressible Cahn-Hilliard-Navier-Stokes phase-field model ⋮
An accurate and parallel method with post-processing boundedness control for solving the anisotropic phase-field dendritic crystal growth model ⋮
A simple and practical finite difference method for the phase-field crystal model with a strong nonlinear vacancy potential on 3D surfaces ⋮
A diffuse interface model and semi-implicit energy stable finite element method for two-phase magnetohydrodynamic flows ⋮
A second-order, uniquely solvable, energy stable BDF numerical scheme for the phase field crystal model ⋮
Optimal rate convergence analysis of a second order scheme for a thin film model with slope selection ⋮
Unconditionally energy stable large time stepping method for the \(L^2\)-gradient flow based ternary phase-field model with precise nonlocal volume conservation ⋮
Preconditioned steepest descent methods for some nonlinear elliptic equations involving p-Laplacian terms ⋮
Error analysis of a decoupled, linear stabilization scheme for the Cahn-Hilliard model of two-phase incompressible flows ⋮
Unconditionally stable finite difference, nonlinear multigrid simulation of the Cahn-Hilliard-Hele-Shaw system of equations ⋮
Linearly first- and second-order, unconditionally energy stable schemes for the phase field crystal model ⋮
Efficient modified stabilized invariant energy quadratization approaches for phase-field crystal equation ⋮
A non-uniform time-stepping convex splitting scheme for the time-fractional Cahn-Hilliard equation ⋮
Two finite difference schemes for the phase field crystal equation ⋮
Convex splitting method for the calculation of transition states of energy functional ⋮
Energy stable numerical schemes for the fractional-in-space Cahn-Hilliard equation ⋮
A new space-time discretization for the Swift-Hohenberg equation that strictly respects the Lyapunov functional ⋮
Deformation and coalescence of ferrodroplets in Rosensweig model using the phase field and modified level set approaches under uniform magnetic fields ⋮
Novel mass-conserving Allen-Cahn equation for the boundedness of an order parameter ⋮
A novel linear, unconditional energy stable scheme for the incompressible Cahn-Hilliard-Navier-Stokes phase-field model ⋮
Energy and entropy preserving numerical approximations of thermodynamically consistent crystal growth models ⋮
Numerical methods for porous medium equation by an energetic variational approach ⋮
An adaptive time-stepping strategy for solving the phase field crystal model ⋮
A convergent convex splitting scheme for the periodic nonlocal Cahn-Hilliard equation ⋮
Error estimates for second-order SAV finite element method to phase field crystal model ⋮
Stability and error estimate of the operator splitting method for the phase field crystal equation ⋮
Decoupled, non-iterative, and unconditionally energy stable large time stepping method for the three-phase Cahn-Hilliard phase-field model ⋮
A weakly nonlinear, energy stable scheme for the strongly anisotropic Cahn-Hilliard equation and its convergence analysis ⋮
An improved error analysis for a second-order numerical scheme for the Cahn-Hilliard equation ⋮
Efficient second-order unconditionally stable numerical schemes for the modified phase field crystal model with long-range interaction ⋮
Highly efficient and stable numerical algorithm for a two-component phase-field crystal model for binary alloys ⋮
Convergence analysis and numerical implementation of a second order numerical scheme for the three-dimensional phase field crystal equation ⋮
An energy-conserving second order numerical scheme for nonlinear hyperbolic equation with an exponential nonlinear term ⋮
Supplementary variable method for thermodynamically consistent partial differential equations ⋮
Regularized linear schemes for the molecular beam epitaxy model with slope selection ⋮
Energy-stable predictor-corrector schemes for the Cahn-Hilliard equation ⋮
Higher-order Cahn-Hilliard equations with dynamic boundary conditions ⋮
Efficient linear, stabilized, second-order time marching schemes for an anisotropic phase field dendritic crystal growth model ⋮
New efficient time-stepping schemes for the Navier-Stokes-Cahn-Hilliard equations ⋮
Error analysis of a mixed finite element method for a Cahn-Hilliard-Hele-Shaw system ⋮
Second order linear thermodynamically consistent approximations to nonlocal phase field porous media models ⋮
Novel linear decoupled and unconditionally energy stable numerical methods for the modified phase field crystal model ⋮
A second order energy stable scheme for the Cahn-Hilliard-Hele-Shaw equations ⋮
Error estimates of energy stable numerical schemes for Allen-Cahn equations with nonlocal constraints ⋮
Efficient numerical schemes with unconditional energy stabilities for the modified phase field crystal equation ⋮
Stable second-order schemes for the space-fractional Cahn-Hilliard and Allen-Cahn equations ⋮
Linear second order energy stable schemes for phase field crystal growth models with nonlocal constraints ⋮
Maximum principle preserving schemes for binary systems with long-range interactions ⋮
On efficient numerical schemes for a two-mode phase field crystal model with face-centered-cubic (FCC) ordering structure ⋮
Efficient and accurate numerical scheme for a magnetic-coupled phase-field-crystal model for ferromagnetic solid materials ⋮
Fast, unconditionally energy stable large time stepping method for a new Allen-Cahn type square phase-field crystal model ⋮
Efficient energy stable schemes for isotropic and strongly anisotropic Cahn-Hilliard systems with the Willmore regularization ⋮
A uniquely solvable, energy stable numerical scheme for the functionalized Cahn-Hilliard equation and its convergence analysis ⋮
An energy stable finite element scheme for the three-component Cahn-Hilliard-type model for macromolecular microsphere composite hydrogels ⋮
An energy stable, hexagonal finite difference scheme for the 2D phase field crystal amplitude equations ⋮
Convergence analysis of a second-order semi-implicit projection method for Landau-Lifshitz equation ⋮
A fast Galerkin finite element method for a space-time fractional Allen-Cahn equation ⋮
Error analysis of full-discrete invariant energy quadratization schemes for the Cahn-Hilliard type equation ⋮
A second order accurate scalar auxiliary variable (SAV) numerical method for the square phase field crystal equation ⋮
Numerical approximation of the two-component PFC models for binary colloidal crystals: efficient, decoupled, and second-order unconditionally energy stable schemes ⋮
A second order energy stable BDF numerical scheme for the Swift-Hohenberg equation ⋮
Two fast and efficient linear semi-implicit approaches with unconditional energy stability for nonlocal phase field crystal equation ⋮
Convergence analysis for the invariant energy quadratization (IEQ) schemes for solving the Cahn-Hilliard and Allen-Cahn equations with general nonlinear potential ⋮
Local energy dissipation rate preserving approximations to driven gradient flows with applications to graphene growth ⋮
Explicit third-order unconditionally structure-preserving schemes for conservative Allen-Cahn equations ⋮
Linear and energy stable schemes for the Swift-Hohenberg equation with quadratic-cubic nonlinearity based on a modified scalar auxiliary variable approach ⋮
The stabilized-trigonometric scalar auxiliary variable approach for gradient flows and its efficient schemes ⋮
Linear and unconditionally energy stable schemes for the binary fluid-surfactant phase field model ⋮
A fully-discrete decoupled finite element method for the conserved Allen-Cahn type phase-field model of three-phase fluid flow system ⋮
An iteration solver for the Poisson-Nernst-Planck system and its convergence analysis ⋮
Efficient linear and unconditionally energy stable schemes for the modified phase field crystal equation ⋮
Energy stable numerical schemes for ternary Cahn-Hilliard system ⋮
Numerical approximation of the square phase-field crystal dynamics on the three-dimensional objects ⋮
Error estimates for the scalar auxiliary variable (SAV) schemes to the modified phase field crystal equation ⋮
Second-order stabilized semi-implicit energy stable schemes for bubble assemblies in binary and ternary systems ⋮
\(C^1 \)-VEM for some variants of the Cahn-Hilliard equation: a numerical exploration ⋮
Optimized Ventcel-Schwarz methods for the Cahn-Hilliard equation discretized by the stabilized linear Crank-Nicolson scheme ⋮
Thermal-fluid topology optimization with unconditional energy stability and second-order accuracy via phase-field model ⋮
A structure-preserving and variable-step BDF2 Fourier pseudo-spectral method for the two-mode phase field crystal model ⋮
A second-order BDF scheme for the Swift-Hohenberg gradient flows with quadratic-cubic nonlinearity and vacancy potential ⋮
Robust exponential attractors for the modified phase-field crystal equation ⋮
On the phase-field-crystal model with logarithmic nonlinear terms