A variant of scalar auxiliary variable approaches for gradient flows

DOI10.1016/j.jcp.2019.05.037zbMath1452.65197OpenAlexW2949558036WikidataQ127639183 ScholiaQ127639183MaRDI QIDQ2222345

Dianming Hou, Mejdi Aza ıïez, Chuanju Xu

Publication date: 26 January 2021

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jcp.2019.05.037

zbMATH Keywords

unconditional stabilityspectral methodtime-stepping schemegradient flows

Mathematics Subject Classification ID

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)

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Cites Work

• On second order semi-implicit Fourier spectral methods for 2D Cahn-Hilliard equations
• Finite element approximation of nematic liquid crystal flows using a saddle-point structure
• Numerical approximations of Allen-Cahn and Cahn-Hilliard equations
• Unconditionally stable schemes for equations of thin film epitaxy
• Applications of semi-implicit Fourier-spectral method to phase field equations
• Linear, first and second-order, unconditionally energy stable numerical schemes for the phase field model of homopolymer blends
• Numerical approximations for the molecular beam epitaxial growth model based on the invariant energy quadratization method
• The scalar auxiliary variable (SAV) approach for gradient flows
• On linear schemes for a Cahn-Hilliard diffuse interface model
• An Adaptive Time-Stepping Strategy for the Molecular Beam Epitaxy Models
• The Global Dynamics of Discrete Semilinear Parabolic Equations
• Efficient Spectral-Galerkin Method I. Direct Solvers of Second- and Fourth-Order Equations Using Legendre Polynomials
• A diffuse-interface method for simulating two-phase flows of complex fluids
• DIFFUSE-INTERFACE METHODS IN FLUID MECHANICS
• Thin film epitaxy with or without slope selection
• TWO-PHASE BINARY FLUIDS AND IMMISCIBLE FLUIDS DESCRIBED BY AN ORDER PARAMETER
• Free Energy of a Nonuniform System. I. Interfacial Free Energy
• Numerical approximations for a phase field dendritic crystal growth model based on the invariant energy quadratization approach
• Stability Analysis of Large Time‐Stepping Methods for Epitaxial Growth Models