Error analysis of the Crank-Nicolson SAV method for the Allen-Cahn equation on variable grids

DOI10.1016/j.aml.2021.107768OpenAlexW3209098824MaRDI QIDQ2060839

Fan Yu, Minghua Chen

Publication date: 13 December 2021

Published in: Applied Mathematics Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aml.2021.107768

zbMATH Keywords

convergence analysisAllen-Cahn equationvariable step sizesscalar auxiliary variable

Mathematics Subject Classification ID

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) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06)

Related Items (2)

A novel adaptive Crank-Nicolson-type scheme for the time fractional Allen-Cahn model ⋮ Analysis of (shifted) piecewise quadratic polynomial collocation for nonlocal diffusion model

Cites Work

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• The scalar auxiliary variable (SAV) approach for gradient flows
• Unconditional energy dissipation and error estimates of the SAV Fourier spectral method for nonlinear fractional generalized wave equation
• Error estimates for second-order SAV finite element method to phase field crystal model
• Spectral Methods
• Convergence and Error Analysis for the Scalar Auxiliary Variable (SAV) Schemes to Gradient Flows
• On Energy Stable, Maximum-Principle Preserving, Second-Order BDF Scheme with Variable Steps for the Allen--Cahn Equation
• The Energy Technique for the Six-Step BDF Method
• Energy-Decaying Extrapolated RK--SAV Methods for the Allen--Cahn and Cahn--Hilliard Equations
• Adaptive Second-Order Crank--Nicolson Time-Stepping Schemes for Time-Fractional Molecular Beam Epitaxial Growth Models

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