An energy stable fourth order finite difference scheme for the Cahn-Hilliard equation

DOI10.1016/j.cam.2018.05.039zbMath1416.65256arXiv1712.06210OpenAlexW2962906715WikidataQ129756883 ScholiaQ129756883MaRDI QIDQ2315907

Cheng Wang, Kelong Cheng, Wenqiang Feng, Steven M. Wise

Publication date: 26 July 2019

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1712.06210

zbMATH Keywords

Cahn-Hilliard equation energy stability optimal rate convergence analysis second order accuracy in time long stencil fourth order finite difference approximation preconditioned steepest descent iteration

Mathematics Subject Classification ID

Numerical optimization and variational techniques (65K10) Nonlinear parabolic equations (35K55) Initial-boundary value problems for higher-order parabolic equations (35K35) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12)

Related Items (only showing first 100 items - show all)

Recovery type a posteriori error estimation of an adaptive finite element method for Cahn-Hilliard equation ⋮ A BDF2 energy‐stable scheme for the binary fluid‐surfactant hydrodynamic model ⋮ Linear and nonlinear Dirichlet–Neumann methods in multiple subdomains for the Cahn–Hilliard equation ⋮ Analysis of the linearly energy- and mass-preserving finite difference methods for the coupled Schrödinger-Boussinesq equations ⋮ A novel second-order linear scheme for the Cahn-Hilliard-Navier-Stokes equations ⋮ Arbitrarily high-order linear energy stable schemes for gradient flow models ⋮ A positivity-preserving, energy stable scheme for a ternary Cahn-Hilliard system with the singular interfacial parameters ⋮ An energy stable linear numerical method for thermodynamically consistent modeling of two-phase incompressible flow in porous media ⋮ A stabilized fully-discrete scheme for phase field crystal equation ⋮ A linearity-preserving technique for finite volume schemes of anisotropic diffusion problems on polygonal meshes ⋮ Motion by mean curvature with constraints using a modified Allen-Cahn equation ⋮ On novel linear schemes for the Cahn-Hilliard equation based on an improved invariant energy quadratization approach ⋮ A Modified Crank-Nicolson Numerical Scheme for the Flory-Huggins Cahn-Hilliard Model ⋮ Optimal rate convergence analysis of a numerical scheme for the ternary Cahn-Hilliard system with a Flory-Huggins-deGennes energy potential ⋮ Mesh-robustness of an energy stable BDF2 scheme with variable steps for the Cahn-Hilliard model ⋮ Efficient and practical phase-field method for the incompressible multi-component fluids on 3D surfaces with arbitrary shapes ⋮ A second-order maximum bound principle preserving operator splitting method for the Allen-Cahn equation with applications in multi-phase systems ⋮ An accurate and parallel method with post-processing boundedness control for solving the anisotropic phase-field dendritic crystal growth model ⋮ A linearized finite difference scheme for the Richards equation under variable-flux boundary conditions ⋮ Optimal rate convergence analysis of a second order scheme for a thin film model with slope selection ⋮ Efficient fully decoupled and second-order time-accurate scheme for the Navier-Stokes coupled Cahn-Hilliard Ohta-Kawaski phase-field model of diblock copolymer melt ⋮ Unconditional convergence analysis of stabilized FEM-SAV method for Cahn-Hilliard equation ⋮ Stability of high order finite difference and local discontinuous Galerkin schemes with explicit-implicit-null time-marching for high order dissipative and dispersive equations ⋮ A new magnetic-coupled Cahn-Hilliard phase-field model for diblock copolymers and its numerical approximations ⋮ Efficient numerical scheme for a new hydrodynamically-coupled conserved Allen-Cahn type Ohta-Kawaski phase-field model for diblock copolymer melt ⋮ Diagonalization based parallel-in-time method for a class of fourth order time dependent PDEs ⋮ An efficient and physically consistent numerical method for the Maxwell–Stefan–Darcy model of two‐phase flow in porous media ⋮ Compatible Energy Dissipation of the Variable-Step \({\boldsymbol{L1}}\) Scheme for the Space-Time Fractional Cahn-Hilliard Equation ⋮ Three decoupled, second-order accurate, and energy stable schemes for the conserved Allen-Cahn-type block copolymer (BCP) model ⋮ An energy stable, conservative and bounds‐preserving numerical method for thermodynamically consistent modeling of incompressible two‐phase flow in porous media with rock compressibility ⋮ High order accurate and convergent numerical scheme for the strongly anisotropic Cahn–Hilliard model ⋮ Stability of Spectral Collocation Schemes with Explicit-Implicit-Null Time-Marching for ConvectionDiffusion and Convection-Dispersion Equations ⋮ Superconvergence analysis of an energy stable scheme with three step backward differential formula‐finite element method for nonlinear reaction–diffusion equation ⋮ An ALE meshfree method for surface PDEs coupling with forced mean curvature flow ⋮ High-order compact finite difference schemes for solving the regularized long-wave equation ⋮ Efficient modified stabilized invariant energy quadratization approaches for phase-field crystal equation ⋮ High-order semi-implicit schemes for evolutionary partial differential equations with higher order derivatives ⋮ A stabilized second order exponential time differencing multistep method for thin film growth model without slope selection ⋮ Numerical analysis of a second-order energy-stable finite element method for the Swift-Hohenberg equation ⋮ A linear second-order maximum bound principle-preserving BDF scheme for the Allen-Cahn equation with a general mobility ⋮ Double stabilizations and convergence analysis of a second-order linear numerical scheme for the nonlocal Cahn-Hilliard equation ⋮ Unconditional superconvergence analysis of an energy-preserving finite element scheme for nonlinear BBM equation ⋮ Local volume-conservation-improved diffuse interface model for simulation of Rayleigh-Plateau fluid instability ⋮ Phase field modeling and computation of vesicle growth or shrinkage ⋮ Efficient IMEX and consistently energy-stable methods of diffuse-interface models for incompressible three-component flows ⋮ Linear and conservative IMEX Runge-Kutta finite difference schemes with provable energy stability for the Cahn-Hilliard model in arbitrary domains ⋮ Second order stabilized semi-implicit scheme for the Cahn-Hilliard model with dynamic boundary conditions ⋮ An adaptive discontinuous finite volume element method for the Allen-Cahn equation ⋮ Superconvergence analysis of a two-grid method for an energy-stable Ciarlet-Raviart type scheme of Cahn-Hilliard equation ⋮ An unconditionally stable second-order accurate method for systems of Cahn-Hilliard equations ⋮ An upwind DG scheme preserving the maximum principle for the convective Cahn-Hilliard model ⋮ Convergence of substructuring methods for the Cahn-Hilliard equation ⋮ An unconditionally stable scheme for the Allen-Cahn equation with high-order polynomial free energy ⋮ A second order fully-discrete linear energy stable scheme for a binary compressible viscous fluid model ⋮ A weakly nonlinear, energy stable scheme for the strongly anisotropic Cahn-Hilliard equation and its convergence analysis ⋮ An energy stable \(C^0\) finite element scheme for a quasi-incompressible phase-field model of moving contact line with variable density ⋮ An improved error analysis for a second-order numerical scheme for the Cahn-Hilliard equation ⋮ Unconditionally energy stable second-order numerical schemes for the functionalized Cahn-Hilliard gradient flow equation based on the SAV approach ⋮ Unnamed Item ⋮ High order accurate in time, fourth order finite difference schemes for the harmonic mapping flow ⋮ A meshless technique based on generalized moving least squares combined with the second-order semi-implicit backward differential formula for numerically solving time-dependent phase field models on the spheres ⋮ Superconvergence analysis of an energy stable scheme for nonlinear reaction-diffusion equation with BDF mixed FEM ⋮ An improved scalar auxiliary variable (SAV) approach for the phase-field surfactant model ⋮ An efficient stabilized multiple auxiliary variables method for the Cahn-Hilliard-Darcy two-phase flow system ⋮ A linear second-order in time unconditionally energy stable finite element scheme for a Cahn-Hilliard phase-field model for two-phase incompressible flow of variable densities ⋮ 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 ⋮ 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 Third Order BDF Energy Stable Linear Scheme for the No-Slope-Selection Thin Film Model ⋮ Error analysis of a fully discrete Morley finite element approximation for the Cahn-Hilliard equation ⋮ Unnamed Item ⋮ Linear energy stable and maximum principle preserving semi-implicit scheme for Allen-Cahn equation with double well potential ⋮ Superconvergence analysis of a MFEM for BBM equation with a stable scheme ⋮ Stabilized energy factorization approach for Allen-Cahn equation with logarithmic Flory-Huggins potential ⋮ An efficient second-order energy stable BDF scheme for the space fractional Cahn-Hilliard equation ⋮ Numerical study of the ternary Cahn-Hilliard fluids by using an efficient modified scalar auxiliary variable approach ⋮ Error analysis of full-discrete invariant energy quadratization schemes for the Cahn-Hilliard type equation ⋮ Arbitrarily High-Order Unconditionally Energy Stable Schemes for Thermodynamically Consistent Gradient Flow Models ⋮ A second order energy stable BDF numerical scheme for the Swift-Hohenberg equation ⋮ Operator-compensation methods with mass and energy conservation for solving the Gross-Pitaevskii equation ⋮ 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 ⋮ Tailored finite point method for diffusion equations with interfaces on distorted meshes ⋮ Efficient, non-iterative, and second-order accurate numerical algorithms for the anisotropic Allen-Cahn equation with precise nonlocal mass conservation ⋮ Efficient decoupled second-order numerical scheme for the flow-coupled Cahn-Hilliard phase-field model of two-phase flows ⋮ Modeling and Simulation of a Ternary System for Macromolecular Microsphere Composite Hydrogels ⋮ Structure-Preserving, Energy Stable Numerical Schemes for a Liquid Thin Film Coarsening Model ⋮ A new energy-stable nonconforming finite element method for Sobolev equation with Burgers' type nonlinearity ⋮ Energy stable higher-order linear ETD multi-step methods for gradient flows: application to thin film epitaxy ⋮ A second order accuracy in time, Fourier pseudo-spectral numerical scheme for ``good Boussinesq equation ⋮ Optimal convergence analysis of a second order scheme for a thin film model without slope selection ⋮ Energy stable numerical schemes for ternary Cahn-Hilliard system ⋮ A third order exponential time differencing numerical scheme for no-slope-selection epitaxial thin film model with energy stability ⋮ Numerical framework for the Caputo time-fractional diffusion equation with fourth order derivative in space ⋮ Convergence to equilibrium for time and space discretizations of the Cahn-Hilliard equation ⋮ An efficient time-dependent auxiliary variable approach for the three-phase conservative Allen-Cahn fluids ⋮ Decoupled, Linear, and Unconditionally Energy Stable Fully Discrete Finite Element Numerical Scheme for a Two-Phase Ferrohydrodynamics Model ⋮ A structure-preserving and variable-step BDF2 Fourier pseudo-spectral method for the two-mode phase field crystal model ⋮ A Third Order Accurate in Time, BDF-Type Energy Stable Scheme for the Cahn-Hilliard Equation

Cites Work

This page was built for publication: An energy stable fourth order finite difference scheme for the Cahn-Hilliard equation