Optimal error estimates of a SAV-FEM for the Cahn-Hilliard-Navier-Stokes model

DOI10.1016/j.cam.2023.115577OpenAlexW4386865605MaRDI QIDQ6079950

Yaoyao Chen, Nian-Yu Yi, Jinting Yang

Publication date: 30 October 2023

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2023.115577

zbMATH Keywords

error estimatesfinite element methodCahn-Hilliard-Navier-Stokes equationsEuler semi-implicit schemescalar auxiliary variable

Mathematics Subject Classification ID

Basic methods in fluid mechanics (76Mxx) Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems (65Mxx) Incompressible viscous fluids (76Dxx)

Cites Work

• Unnamed Item
• A second order in time, uniquely solvable, unconditionally stable numerical scheme for Cahn-Hilliard-Navier-Stokes equation
• Energy stable schemes for Cahn-Hilliard phase-field model of two-phase incompressible flows
• A diffuse-interface model for axisymmetric immiscible two-phase flow
• An efficient semi-implicit immersed boundary method for the Navier-Stokes equations
• Nonlinear Galerkin methods and mixed finite elements: Two-grid algorithms for the Navier-Stokes equations
• Conservative multigrid methods for Cahn--Hilliard fluids.
• Linear, second order and unconditionally energy stable schemes for the viscous Cahn-Hilliard equation with hyperbolic relaxation using the invariant energy quadratization method
• Convergence analysis and error estimates for a second order accurate finite element method for the Cahn-Hilliard-Navier-Stokes system
• Numerical approximations for the molecular beam epitaxial growth model based on the invariant energy quadratization method
• Analysis of the grad-div stabilization for the time-dependent Navier-Stokes equations with inf-sup stable finite elements
• The scalar auxiliary variable (SAV) approach for gradient flows
• Unconditional stability and optimal error estimates of Euler implicit/explicit-SAV scheme for the Navier-Stokes equations
• Optimal error estimates for the scalar auxiliary variable finite-element schemes for gradient flows
• Numerical approximation of incompressible Navier-Stokes equations based on an auxiliary energy variable
• An unconditionally energy-stable scheme based on an implicit auxiliary energy variable for incompressible two-phase flows with different densities involving only precomputable coefficient matrices
• Error estimates for time discretizations of Cahn-Hilliard and Allen-Cahn phase-field models for two-phase incompressible flows
• Analysis of a Mixed Finite Element Method for a Cahn--Hilliard--Darcy--Stokes System
• 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
• Analysis of finite element approximations of a phase field model for two-phase fluids
• Fully Discrete Finite Element Approximations of the Navier--Stokes--Cahn-Hilliard Diffuse Interface Model for Two-Phase Fluid Flows
• On Error Estimates of Projection Methods for Navier–Stokes Equations: First-Order Schemes
• Two-Level Method Based on Finite Element and Crank-Nicolson Extrapolation for the Time-Dependent Navier-Stokes Equations
• A diffuse-interface method for simulating two-phase flows of complex fluids
• Convergence and Error Analysis for the Scalar Auxiliary Variable (SAV) Schemes to Gradient Flows
• Long time stability and convergence for fully discrete nonlinear galerkin methods
• On Error Estimates of the Penalty Method for Unsteady Navier–Stokes Equations
• On fully decoupled MSAV schemes for the Cahn–Hilliard–Navier–Stokes model of two-phase incompressible flows
• Error Analysis of the SAV-MAC Scheme for the Navier--Stokes Equations
• Free Energy of a Nonuniform System. I. Interfacial Free Energy
• Unconditional convergence of the Euler semi-implicit scheme for the three-dimensional incompressible MHD equations
• Numerical approximations for a phase field dendritic crystal growth model based on the invariant energy quadratization approach
• Stability and Convergence of the Crank–Nicolson/Adams–Bashforth scheme for the Time‐Dependent Navier–Stokes Equations
• On Convergent Schemes for Diffuse Interface Models for Two-Phase Flow of Incompressible Fluids with General Mass Densities
• Galerkin Finite Element Methods for Parabolic Problems
• Stability and error analysis for a spectral Galerkin method for the Navier‐Stokes equations with H² or H¹ initial data

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