The long-time \(L^2\) and \(H^1\) stability of linearly extrapolated second-order time-stepping schemes for the 2D incompressible Navier-Stokes equations

DOI10.1016/J.AMC.2018.09.022zbMath1428.76097OpenAlexW2896208657WikidataQ129111773 ScholiaQ129111773MaRDI QIDQ2008031

Sean Breckling, Sidney Shields

Publication date: 22 November 2019

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

Full work available at URL: https://doi.org/10.1016/j.amc.2018.09.022

zbMATH Keywords

finite element methodsNavier Stokes equationslong time stability

Mathematics Subject Classification ID

Navier-Stokes equations for incompressible viscous fluids (76D05) Navier-Stokes equations (35Q30) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Finite element methods applied to problems in fluid mechanics (76M10) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60)

Related Items (2)

Long-time \(H^1\)-stability of BDF2 time stepping for 2D Navier-Stokes equations ⋮ A Crank-Nicolson discontinuous Galerkin pressure-projection method for the hydrodynamic and sediment transport model

Uses Software

• RODAS
• FEniCS
• UFL
• Unnamed Item

Cites Work

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• An efficient second order in time scheme for approximating long time statistical properties of the two-dimensional Navier-Stokes equations
• Unconditional long-time stability of a velocity-vorticity method for the 2D Navier-Stokes equations
• Quadratic divergence-free finite elements on Powell--Sabin tetrahedral grids
• A numerical solution of the Navier-Stokes equations using the finite element technique
• Unconditional stability and long-term behavior of transient algorithms for the incompressible Navier-Stokes and Euler equations
• An optimally accurate discrete regularization for second order timestepping methods for Navier-Stokes equations
• A note on the importance of mass conservation in long-time stability of Navier-Stokes simulations using finite elements
• Long Time Stability of a Classical Efficient Scheme for Two-dimensional Navier–Stokes Equations
• Divergence-free finite elements on tetrahedral grids for $k\ge6$
• Finite-Element Approximation of the Nonstationary Navier–Stokes Problem. Part IV: Error Analysis for Second-Order Time Discretization
• Gmsh: A 3-D finite element mesh generator with built-in pre- and post-processing facilities
• Finite Element Approximation of the Nonstationary Navier–Stokes Problem, Part II: Stability of Solutions and Error Estimates Uniform in Time
• The Scott-Vogelius finite elements revisited
• A new family of stable mixed finite elements for the 3D Stokes equations
• Long time stability and convergence for fully discrete nonlinear galerkin methods
• On the stability at all times of linearly extrapolated BDF2 timestepping for multiphysics incompressible flow problems
• Long-Term Stability Estimates and Existence of a Global Attractor in a Finite Element Approximation of the Navier–Stokes Equations with Numerical Subgrid Scale Modeling
• On the long‐time stability of the Crank–Nicolson scheme for the 2D Navier–Stokes equations
• On the Long-Time Stability of the Implicit Euler Scheme for the Two-Dimensional Navier--Stokes Equations
• Unified form language

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