Low order nonconforming mixed finite element method for nonstationary incompressible Navier-Stokes equations

DOI10.1007/s10483-016-2120-8zbMath1348.76057OpenAlexW2500325547MaRDI QIDQ333935

Xin Liao, Chao Xu, Dong-Yang Shi

Publication date: 31 October 2016

Published in: AMM. Applied Mathematics and Mechanics. (English Edition) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10483-016-2120-8

zbMATH Keywords

constrained \(Q_{1}^{\mathrm{rot}}\) nonconforming finite element (FE)nonstationary incompressible Navier-Stokes equationsuperconvergent error estimate

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 (9)

The supercloseness property of the Stokes projection for the transient Navier-Stokes equations and global superconvergence analysis ⋮ Superconvergent analysis of a nonconforming mixed finite element method for non-stationary conduction-convection problem ⋮ Superconvergence analysis of low order nonconforming finite element methods for variational inequality problem with displacement obstacle ⋮ A nonconforming finite element method for the stationary Smagorinsky model ⋮ Superconvergent analysis of a nonconforming mixed finite element method for time-dependent damped Navier-Stokes equations ⋮ A new two-grid nonconforming mixed finite element method for nonlinear Benjamin-Bona-Mahoney equation ⋮ Lowest order virtual element approximations for transient Stokes problem on polygonal meshes ⋮ Analytical solutions for buckling of size-dependent Timoshenko beams ⋮ A novel approach of superconvergence analysis of the bilinear-constant scheme for time-dependent Stokes equations

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Finite difference streamline diffusion method using nonconforming space for incompressible time-dependent Navier-Stokes equations
• The Crouzeix-Raviart type nonconforming finite element method for the nonstationary Navier-Stokes equations on anisotropic meshes
• A new nonconforming mixed finite element scheme for the stationary Navier-Stokes equations
• A fully discrete stabilized finite element method for the time-dependent Navier-Stokes equations
• A new stabilized finite element method for the transient Navier-Stokes equations
• Superconvergence analysis of the nonconforming quadrilateral linear-constant scheme for Stokes equations
• Error estimate of the \(P_1\) nonconforming finite element method for the penalized unsteady Navier-Stokes equations
• Nonconforming mixed finite element approximation to the stationary Navier-Stokes equations on anisotropic meshes
• An analysis of a mixed finite element method for the Navier-Stokes equations
• Superconvergence analysis for the Navier-Stokes equations
• Superconvergence of nonconforming finite element penalty scheme for Stokes problem using \(L^2\) projection method
• Stabilized finite element method based on the Crank--Nicolson extrapolation scheme for the time-dependent Navier--Stokes equations
• A Conforming Finite Element Method for the Time-Dependent Navier–Stokes Equations
• Finite Element Approximation of the Nonstationary Navier–Stokes Problem. I. Regularity of Solutions and Second-Order Error Estimates for Spatial Discretization
• Simple nonconforming quadrilateral Stokes element
• Conforming and nonconforming finite element methods for solving the stationary Stokes equations I
• On the Accuracy of Nonconforming Quadrilateral Q₁ Element Approximation for the Navier--Stokes Problem
• Superconvergence of nonconforming finite element method for the Stokes equations
• Optimal error estimate of the penalty finite element method for the time-dependent Navier-Stokes equations
• A New Error Analysis of Characteristics-Mixed FEMs for Miscible Displacement in Porous Media
• A Finite Element Variational Multiscale Method for the Navier--Stokes Equations
• A new linearly extrapolated Crank-Nicolson time-stepping scheme for the Navier-Stokes equations

This page was built for publication: Low order nonconforming mixed finite element method for nonstationary incompressible Navier-Stokes equations