Unconditional stability and optimal error estimates of Euler implicit/explicit-SAV scheme for the Navier-Stokes equations

DOI10.1007/s10915-021-01681-yzbMath1490.65217OpenAlexW3214418250MaRDI QIDQ2053329

Yanyan Li

Publication date: 29 November 2021

Published in: Journal of Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10915-021-01681-y

zbMATH Keywords

unconditional stabilityoptimal error estimatestime-dependent Navier-Stokes equationsscalar auxiliary variableEuler explicit/implicit scheme

Mathematics Subject Classification ID

Navier-Stokes equations for incompressible viscous fluids (76D05) 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) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15)

Related Items

Analysis of divergence-free 𝐻¹ conforming FEM with IMEX-SAV scheme for the Navier-Stokes equations at high Reynolds number ⋮ Numerical analysis of the SAV scheme for the EMAC formulation of the time-dependent Navier-Stokes equations ⋮ Behavior of Lagrange‐Galerkin solutions to the Navier‐Stokes problem for small time increment ⋮ Optimal error estimates of a SAV-FEM for the Cahn-Hilliard-Navier-Stokes model ⋮ Unconditional stability and error analysis of an Euler IMEX-SAV scheme for the micropolar Navier-Stokes equations ⋮ Fully decoupled linear BDF2 scheme for the penalty incompressible Ericksen-Leslie equations ⋮ Unconditional stability of first and second orders implicit/explicit schemes for the natural convection equations ⋮ Unnamed Item

Uses Software

• XTOR-2F
• XTOR

Cites Work

• Unnamed Item
• A penalty finite element method based on the Euler implicit/explicit scheme for the time-dependent Navier-Stokes equations
• An efficient semi-implicit immersed boundary method for the Navier-Stokes equations
• An implicit high-order hybridizable discontinuous Galerkin method for nonlinear convection-diffusion equations
• Solution of the incompressible Navier-Stokes equations by the nonlinear Galerkin method
• Nonlinear Galerkin methods and mixed finite elements: Two-grid algorithms for the Navier-Stokes equations
• Linear, second order and unconditionally energy stable schemes for the viscous Cahn-Hilliard equation with hyperbolic relaxation using the invariant energy quadratization method
• 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
• High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method
• XTOR-2F: a fully implicit Newton-Krylov solver applied to nonlinear 3D extended MHD in tokamaks
• An explicit-implicit finite element model for the numerical solution of incompressible Navier-Stokes equations on moving grids
• 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
• Local discontinuous Galerkin methods with implicit-explicit multistep time-marching for solving the nonlinear Cahn-Hilliard equation
• \(H^2\)-stability of the first order fully discrete schemes for the time-dependent Navier-Stokes equations
• The almost unconditional convergence of the Euler implicit/explicit scheme for the three dimensional nonstationary Navier-Stokes equations
• Two-level stabilized finite element methods for the steady Navier-Stokes problem
• Error analysis of linearized semi-implicit Galerkin finite element methods for nonlinear parabolic equations
• The Euler implicit/explicit scheme for the 2D time-dependent Navier-Stokes equations with smooth or non-smooth initial data
• 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
• Finite Element Methods for Navier-Stokes Equations
• Finite Element Approximation of the Nonstationary Navier–Stokes Problem. I. Regularity of Solutions and Second-Order Error Estimates for Spatial Discretization
• On Error Estimates of Projection Methods for Navier–Stokes Equations: First-Order Schemes
• A fully discrete stabilized finite-element method for the time-dependent Navier-Stokes problem
• Approximation of the global attractor for the incompressible Navier-Stokes equations
• 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 projection methods for the Navier-Stokes equations: Second-order schemes
• Error Analysis of the SAV-MAC Scheme for the Navier--Stokes Equations
• Semi-Implicit Formulations of the Navier–Stokes Equations: Application to Nonhydrostatic Atmospheric Modeling
• 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
• Numerical solutions of 2-D steady incompressible driven cavity flow at high Reynolds numbers
• Convergence of the implicit-explicit Euler scheme applied to perturbed dissipative evolution equations
• Energy stability and convergence of SAV block-centered finite difference method for gradient flows
• On the Long-Time Stability of the Implicit Euler Scheme for the Two-Dimensional Navier--Stokes Equations
• A two-grid stabilization method for solving the steady-state Navier-Stokes equations
• On error estimates of some higher order penalty-projection methods for Navier-Stokes equations