A Third Order Accurate in Time, BDF-Type Energy Stable Scheme for the Cahn-Hilliard Equation
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Publication:5864777
DOI10.4208/nmtma.OA-2021-0165zbMath1499.65556OpenAlexW4221005288MaRDI QIDQ5864777
Cheng Wang, Kelong Cheng, Yanmei Wu, Steven M. Wise
Publication date: 8 June 2022
Published in: Numerical Mathematics: Theory, Methods and Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.4208/nmtma.oa-2021-0165
Cahn-Hilliard equationunique solvabilityenergy stabilityoptimal rate convergence analysisthird order backward differentiation formuladiscrete \(L^6_N\) estimate
Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15)
Related Items (8)
A family of structure-preserving exponential time differencing Runge-Kutta schemes for the viscous Cahn-Hilliard equation ⋮ Efficient and energy stable numerical schemes for the two-mode phase field crystal equation ⋮ A second-order exponential time differencing multi-step energy stable scheme for Swift-Hohenberg equation with quadratic-cubic nonlinear term ⋮ A linear second-order maximum bound principle-preserving BDF scheme for the Allen-Cahn equation with a general mobility ⋮ Stability and error estimates of high order BDF-LDG discretizations for the Allen-Cahn equation ⋮ A positivity-preserving, energy stable BDF2 scheme with variable steps for the Cahn-Hilliard equation with logarithmic potential ⋮ A-Stable High-Order Block Implicit Methods for Parabolic Equations ⋮ An adaptive discontinuous finite volume element method for the Allen-Cahn equation
Cites Work
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- An \(H^2\) convergence of a second-order convex-splitting, finite difference scheme for the three-dimensional Cahn-Hilliard equation
- 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
- A linear iteration algorithm for a second-order energy stable scheme for a thin film model without slope selection
- On second order semi-implicit Fourier spectral methods for 2D Cahn-Hilliard equations
- Energy stable higher-order linear ETD multi-step methods for gradient flows: application to thin film epitaxy
- Energy stable numerical schemes for ternary Cahn-Hilliard system
- A second order backward difference method with variable steps for a parabolic problem
- On efficient second order stabilized semi-implicit schemes for the Cahn-Hilliard phase-field equation
- Convergence analysis and error estimates for a second order accurate finite element method for the Cahn-Hilliard-Navier-Stokes system
- Preconditioned steepest descent methods for some nonlinear elliptic equations involving p-Laplacian terms
- The scalar auxiliary variable (SAV) approach for gradient flows
- On the stabilization size of semi-implicit Fourier-spectral methods for 3D Cahn-Hilliard equations
- A second order energy stable scheme for the Cahn-Hilliard-Hele-Shaw equations
- A second order energy stable linear scheme for a thin film model without slope selection
- Stability and convergence analysis of fully discrete Fourier collocation spectral method for 3-D viscous Burgers' equation
- A linear energy stable scheme for a thin film model without slope selection
- An improved error analysis for a second-order numerical scheme for the Cahn-Hilliard equation
- High order accurate in time, fourth order finite difference schemes for the harmonic mapping flow
- An energy stable fourth order finite difference scheme for the Cahn-Hilliard equation
- A third order exponential time differencing numerical scheme for no-slope-selection epitaxial thin film model with energy stability
- A second-order, weakly energy-stable pseudo-spectral scheme for the Cahn-Hilliard equation and its solution by the homogeneous linear iteration method
- Characterizing the Stabilization Size for Semi-Implicit Fourier-Spectral Method to Phase Field Equations
- Long Time Stability of High Order MultiStep Numerical Schemes for Two-Dimensional Incompressible Navier--Stokes Equations
- Simple and Efficient ALE Methods with Provable Temporal Accuracy up to Fifth Order for the Stokes Equations on Time Varying Domains
- Long Time Stability of a Classical Efficient Scheme for Two-dimensional Navier–Stokes Equations
- Analysis of a Mixed Finite Element Method for a Cahn--Hilliard--Darcy--Stokes System
- Convergence analysis for second-order accurate schemes for the periodic nonlocal Allen-Cahn and Cahn-Hilliard equations
- Spectral Methods for Time-Dependent Problems
- Approximation Results for Orthogonal Polynomials in Sobolev Spaces
- Time analyticity and gevrey regularity for solutions of a class of dissipative partial differential equations
- 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
- Stability and convergence of a second-order mixed finite element method for the Cahn–Hilliard equation
- Convergence and Error Analysis for the Scalar Auxiliary Variable (SAV) Schemes to Gradient Flows
- A Second-Order Energy Stable BDF Numerical Scheme for the Cahn-Hilliard Equation
- An Energy Stable BDF2 Fourier Pseudo-Spectral Numerical Scheme for the Square Phase Field Crystal Equation
- A Third Order BDF Energy Stable Linear Scheme for the No-Slope-Selection Thin Film Model
- Free Energy of a Nonuniform System. I. Interfacial Free Energy
- A New Class of Efficient and Robust Energy Stable Schemes for Gradient Flows
- Stability Analysis of Large Time‐Stepping Methods for Epitaxial Growth Models
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