Error analysis of the SAV Fourier-spectral method for the Cahn-Hilliard-Hele-Shaw system

DOI10.1007/s10444-021-09897-0zbMath1482.65199OpenAlexW3200368810MaRDI QIDQ2230590

Nan Zheng, Xiao-Li Li

Publication date: 24 September 2021

Published in: Advances in Computational Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10444-021-09897-0

zbMATH Keywords

error estimatesunconditionally energy stableCahn-Hilliard-Hele-Shawscalar auxiliary variablefully decoupled scheme

Mathematics Subject Classification ID

Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) PDEs in connection with fluid mechanics (35Q35) 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) 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) Other free boundary flows; Hele-Shaw flows (76D27)

Related Items (7)

A second-order backward differentiation formula for the numerical solution of Cahn-Hilliard-Hele-Shaw system ⋮ Two SAV numerical methods for the nonlocal Cahn-Hilliard-Hele-Shaw system ⋮ Fully decoupled linear BDF2 scheme for the penalty incompressible Ericksen-Leslie equations ⋮ A second-order time-accurate unconditionally stable method for a gradient flow for the Modica-Mortola functional ⋮ Highly efficient time-marching method with enhanced energy consistency for the \(L^2\)-gradient flow based two-phase incompressible fluid system ⋮ Phase-field modeling and consistent energy-stable simulation of binary creeping flows in contact with solid ⋮ New efficient and unconditionally energy stable schemes for the Cahn-Hilliard-Brinkman system

Cites Work

• An efficient fully-discrete local discontinuous Galerkin method for the Cahn-Hilliard-Hele-Shaw system
• Radial basis approximation for Newtonian potentials
• Unconditionally stable finite difference, nonlinear multigrid simulation of the Cahn-Hilliard-Hele-Shaw system of equations
• A second order in time, decoupled, unconditionally stable numerical scheme for the Cahn-Hilliard-Darcy system
• The scalar auxiliary variable (SAV) approach for gradient flows
• Numerical analysis of the Cahn-Hilliard equation and approximation for the Hele-Shaw problem
• A phase field model for the mixture of two incompressible fluids and its approximation by a Fourier-spectral method
• Stability and error estimates of the SAV Fourier-spectral method for the phase field crystal equation
• A second-order decoupled energy stable numerical scheme for Cahn-Hilliard-Hele-Shaw system
• Efficient SAV approach for imaginary time gradient flows with applications to one- and multi-component Bose-Einstein condensates
• A Fourier spectral method for fractional-in-space Cahn-Hilliard equation
• A decoupled unconditionally stable numerical scheme for the Cahn-Hilliard-Hele-Shaw system
• Well-posedness of the Hele-Shaw-Cahn-Hilliard system
• Decoupled energy-law preserving numerical schemes for the Cahn-Hilliard-Darcy system
• Convergence analysis of a fully discrete finite difference scheme for the Cahn-Hilliard-Hele-Shaw equation
• Analysis of a Darcy--Cahn--Hilliard Diffuse Interface Model for the Hele-Shaw Flow and Its Fully Discrete Finite Element Approximation
• Spectral Methods
• Efficient and accurate structure preserving schemes for complex nonlinear systems
• 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
• Convergence and Error Analysis for the Scalar Auxiliary Variable (SAV) Schemes to Gradient Flows
• The Exponential Scalar Auxiliary Variable (E-SAV) Approach for Phase Field Models and Its Explicit Computing
• Energy stability and convergence of SAV block-centered finite difference method for gradient flows

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