A uniquely solvable, positivity-preserving and unconditionally energy stable numerical scheme for the functionalized Cahn-Hilliard equation with logarithmic potential
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Publication:6111670
DOI10.1007/s10915-023-02296-1arXiv2210.08501MaRDI QIDQ6111670
Jianyu Jing, Hao Wu, Wenbin Chen
Publication date: 4 August 2023
Published in: Journal of Scientific Computing (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2210.08501
finite difference schemelogarithmic potentialunique solvabilityenergy stabilitypositivity preservingoptimal rate convergence analysishigher order asymptotic expansionfunctionalized Cahn-Hilliard equation
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) Numerical analysis (65-XX)
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Cites Work
- Unnamed Item
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- An \(H^2\) convergence of a second-order convex-splitting, finite difference scheme for the three-dimensional Cahn-Hilliard equation
- An unconditionally energy stable finite difference scheme for a stochastic Cahn-Hilliard equation
- High accuracy solutions to energy gradient flows from material science models
- An adaptive time-stepping strategy for solving the phase field crystal model
- An energy-conserving second order numerical scheme for nonlinear hyperbolic equation with an exponential nonlinear term
- Unconditionally stable finite difference, nonlinear multigrid simulation of the Cahn-Hilliard-Hele-Shaw system of equations
- Curvature driven flow of bi-layer interfaces
- The Cahn-Hilliard equation with logarithmic potentials
- Compact sets in the space \(L^ p(0,T;B)\)
- Numerical analysis of the Cahn-Hilliard equation with a logarithmic free energy
- A practical numerical scheme for the ternary Cahn-Hilliard system with a logarithmic free energy
- Preconditioned steepest descent methods for some nonlinear elliptic equations involving p-Laplacian terms
- A sixth-order phase-field equation with degenerate mobility
- The Cahn-Hilliard-Hele-Shaw system with singular potential
- A uniquely solvable, energy stable numerical scheme for the functionalized Cahn-Hilliard equation and its convergence analysis
- Convergence of the Cahn-Hilliard equation to the Hele-Shaw model
- A phase field approach in the numerical study of the elastic bending energy for vesicle membranes
- Critical points of functionalized Lagrangians
- Highly accurate, linear, and unconditionally energy stable large time-stepping schemes for the functionalized Cahn-Hilliard gradient flow equation
- Analysis of the energy stability for stabilized semi-implicit schemes of the functionalized Cahn-Hilliard mass-conserving gradient flow equation
- On nonnegative solutions for the functionalized Cahn-Hilliard equation with degenerate mobility
- Numerical comparison of modified-energy stable SAV-type schemes and classical BDF methods on benchmark problems for the functionalized Cahn-Hilliard equation
- A structure-preserving, operator splitting scheme for reaction-diffusion equations with detailed balance
- A regularization-free approach to the Cahn-Hilliard equation with logarithmic potentials
- Energy-decreasing exponential time differencing Runge-Kutta methods for phase-field models
- Global-in-time Gevrey regularity solutions for the functionalized Cahn-Hilliard equation
- Unconditionally energy stable second-order numerical schemes for the functionalized Cahn-Hilliard gradient flow equation based on the SAV approach
- A positivity-preserving, energy stable and convergent numerical scheme for the Cahn-Hilliard equation with a Flory-Huggins-deGennes energy
- Existence of pearled patterns in the planar functionalized Cahn-Hilliard equation
- Local discontinuous Galerkin methods for the functionalized Cahn-Hilliard equation
- Convergence to equilibrium for the Cahn-Hilliard equation with a logarithmic free energy
- Existence, bifurcation, and geometric evolution of quasi-bilayers in the multicomponent functionalized Cahn-Hilliard equation
- Asymptotic behavior of a sixth-order Cahn-Hilliard system
- Solving the regularized, strongly anisotropic Cahn-Hilliard equation by an adaptive nonlinear multigrid method
- An efficient two-grid method for the Cahn-Hilliard equation with the concentration-dependent mobility and the logarithmic Flory-Huggins bulk potential
- A review on the Cahn-Hilliard equation: classical results and recent advances in dynamic boundary conditions
- Sharp-Interface Limits of the Cahn--Hilliard Equation with Degenerate Mobility
- Soft Matter Physics
- A phase field formulation of the Willmore problem
- An Energy Stable and Convergent Finite-Difference Scheme for the Modified Phase Field Crystal Equation
- An Adaptive Time-Stepping Strategy for the Molecular Beam Epitaxy Models
- Stability of the Semi-Implicit Method for the Cahn-Hilliard Equation with Logarithmic Potentials
- Weak solutions for the functionalized Cahn–Hilliard equation with degenerate mobility
- Front migration in the nonlinear Cahn-Hilliard equation
- PEM Fuel Cells: A Mathematical Overview
- A new phase-field model for strongly anisotropic systems
- An Energy-Stable and Convergent Finite-Difference Scheme for the Phase Field Crystal Equation
- Stability of the Fourier Method
- The Global Dynamics of Discrete Semilinear Parabolic Equations
- Robust exponential attractors for Cahn‐Hilliard type equations with singular potentials
- Pearling Bifurcations in the Strong Functionalized Cahn--Hilliard Free Energy
- Efficient Energy Stable Schemes with Spectral Discretization in Space for Anisotropic Cahn-Hilliard Systems
- The Cahn–Hilliard–Oono equation with singular potential
- A second‐order energy stable backward differentiation formula method for the epitaxial thin film equation with slope selection
- A Second Order BDF Numerical Scheme with Variable Steps for the Cahn--Hilliard Equation
- The Cahn–Hilliard equation with a concentration dependent mobility: motion by minus the Laplacian of the mean curvature
- On the Cahn-Hilliard equation with a logarithmic free energy
- On the Cahn–Hilliard Equation with Degenerate Mobility
- On a Class of Cahn--Hilliard Models with Nonlinear Diffusion
- 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
- How Do Degenerate Mobilities Determine Singularity Formation in Cahn--Hilliard Equations?
- A Modified Crank-Nicolson Numerical Scheme for the Flory-Huggins Cahn-Hilliard Model
- On a Class of Sixth-Order Cahn--Hilliard-Type Equations with Logarithmic Potential
- Convergence analysis for a stabilized linear semi-implicit numerical scheme for the nonlocal Cahn–Hilliard equation
- Parallel Energy-Stable Solver for a Coupled Allen--Cahn and Cahn--Hilliard System
- On Linear and Unconditionally Energy Stable Algorithms for Variable Mobility Cahn-Hilliard Type Equation with Logarithmic Flory-Huggins Potential
- A Positivity-Preserving Second-Order BDF Scheme for the Cahn-Hilliard Equation with Variable Interfacial Parameters
- Meander and Pearling of Single-Curvature Bilayer Interfaces in the Functionalized Cahn--Hilliard Equation
- Free Energy of a Nonuniform System. I. Interfacial Free Energy
- Competitive Geometric Evolution of Amphiphilic Interfaces
- Geometric evolution of bilayers under the functionalized Cahn–Hilliard equation
- Weak solutions for the Cahn-Hilliard equation with degenerate mobility
