A new class of implicit-explicit BDF\(k\) SAV schemes for general dissipative systems and their error analysis

DOI10.1016/j.cma.2022.114718OpenAlexW4213351654MaRDI QIDQ2138728

Jie Shen, Fukeng Huang

Publication date: 12 May 2022

Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2103.06344

zbMATH Keywords

error analysisdissipative systemenergy stabilitySAV approachhigh-order BDF scheme

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Initial-boundary value problems for higher-order parabolic equations (35K35) Initial-boundary value problems for second-order parabolic equations (35K20) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12)

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Cites Work

• Numerical approximations of Allen-Cahn and Cahn-Hilliard equations
• The scalar auxiliary variable (SAV) approach for gradient flows
• gPAV-based unconditionally energy-stable schemes for the Cahn-Hilliard equation: stability and error analysis
• A second order accurate scalar auxiliary variable (SAV) numerical method for the square phase field crystal equation
• Optimal error estimates for the scalar auxiliary variable finite-element schemes for gradient flows
• Linearly implicit and high-order energy-conserving schemes for nonlinear wave equations
• Stability and error estimates of the SAV Fourier-spectral method for the phase field crystal equation
• The BDF3/EP3 scheme for MBE with no slope selection is stable
• Characterizing the Stabilization Size for Semi-Implicit Fourier-Spectral Method to Phase Field Equations
• Spectral Methods
• Spectral approximation of pattern-forming nonlinear evolution equations with double-well potentials of quadratic growth
• Efficient and accurate structure preserving schemes for complex nonlinear systems
• Multiplier techniques for linear multistep methods
• Maximum Principle Preserving Exponential Time Differencing Schemes for the Nonlocal Allen--Cahn Equation
• Convergence and Error Analysis for the Scalar Auxiliary Variable (SAV) Schemes to Gradient Flows
• Maximum Bound Principles for a Class of Semilinear Parabolic Equations and Exponential Time-Differencing Schemes
• The IEQ and SAV approaches and their extensions for a class of highly nonlinear gradient flow systems
• ON EFFECTIVE NUMERICAL METHODS FOR PHASE-FIELD MODELS
• Error Analysis of the SAV-MAC Scheme for the Navier--Stokes Equations
• A Highly Efficient and Accurate New Scalar Auxiliary Variable Approach for Gradient Flows
• The Energy Technique for the Six-Step BDF Method
• Energy-Decaying Extrapolated RK--SAV Methods for the Allen--Cahn and Cahn--Hilliard Equations
• Free Energy of a Nonuniform System. I. Interfacial Free Energy
• A New Class of Efficient and Robust Energy Stable Schemes for Gradient Flows
• Stability of Implicit-Explicit Backward Difference Formulas For Nonlinear Parabolic Equations
• A posteriorierror control for the Allen–Cahn problem: circumventing Gronwall's inequality
• Energy stability and convergence of SAV block-centered finite difference method for gradient flows

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