A low-order Galerkin finite element method for the Navier-Stokes equations of steady incompressible flow: a stabilization issue and iterative methods.

DOI10.1016/S0045-7825(02)00513-3zbMath1083.76553MaRDI QIDQ1871025

Maxim A. Olshanskij

Publication date: 6 May 2003

Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)

Mathematics Subject Classification ID

Navier-Stokes equations for incompressible viscous fluids (76D05) Finite element methods applied to problems in fluid mechanics (76M10)

Related Items (64)

Analysis and computation of a pressure-robust method for the rotation form of the incompressible Navier-Stokes equations with high-order finite elements ⋮ A unified framework of continuous and discontinuous Galerkin methods for solving the incompressible Navier-Stokes equation ⋮ On the grad-div stabilization for the steady Oseen and Navier-Stokes equations ⋮ ℋ︁-LU factorization in preconditioners for augmented Lagrangian and grad-div stabilized saddle point systems ⋮ Analysis of preconditioned iterative solvers for incompressible flow problems ⋮ New stabilized \(P_1 \times P_0\) finite element methods for nearly inviscid and incompressible flows ⋮ On the convergence of variational multiscale methods based on Newton's iteration for the incompressible flows ⋮ Numerical analysis and computational comparisons of the NS-alpha and NS-omega regularizations ⋮ A discrete projection method for incompressible viscous flow with Coriolis force ⋮ Sensitivity analysis of the grad-div stabilization parameter in finite element simulations of incompressible flow ⋮ Grad-div stablilization for Stokes equations ⋮ Grad-div stabilization for the evolutionary Oseen problem with inf-sup stable finite elements ⋮ Stability in 3d of a sparse Grad-div approximation of the Navier-Stokes equations ⋮ On the determination of the grad-div criterion ⋮ Note on the effect of grad-div stabilization on calculating drag and lift coefficients ⋮ Augmented Lagrangian preconditioner for large-scale hydrodynamic stability analysis ⋮ Modular grad-div stabilization for the incompressible non-isothermal fluid flows ⋮ Saddle point preconditioners for linearized Navier-Stokes equations discretized by a finite volume method ⋮ New connections between finite element formulations of the Navier-Stokes equations ⋮ Error analysis for a vorticity/Bernoulli pressure formulation for the Oseen equations ⋮ Preconditioning sparse grad-div/augmented Lagrangian stabilized saddle point systems ⋮ Mixed finite element methods with convection stabilization for the large eddy simulation of incompressible turbulent flows ⋮ On the Divergence Constraint in Mixed Finite Element Methods for Incompressible Flows ⋮ A cutFEM divergence–free discretization for the stokes problem ⋮ An EMA-conserving, pressure-robust and Re-semi-robust method with A robust reconstruction method for Navier–Stokes ⋮ A modified convective formulation in Navier-Stokes simulations ⋮ A second-order ensemble method based on a blended backward differentiation formula timestepping scheme for time-dependent Navier-Stokes equations ⋮ A structure-preserving integrator for incompressible finite elastodynamics based on a Grad-div stabilized mixed formulation with particular emphasis on stretch-based material models ⋮ A continuum and computational framework for viscoelastodynamics. II: Strain-driven and energy-momentum consistent schemes ⋮ Analysis of the grad-div stabilization for the time-dependent Navier-Stokes equations with inf-sup stable finite elements ⋮ \(H(\operatorname{div})\) conforming methods for the rotation form of the incompressible fluid equations ⋮ A parallel grad-div stabilized finite element algorithm for the Stokes equations with damping ⋮ An alternative HSS preconditioner for the unsteady incompressible Navier-Stokes equations in rotation form ⋮ New subgrid artificial viscosity Galerkin methods for the Navier-Stokes equations ⋮ On the parameter choice in grad-div stabilization for the Stokes equations ⋮ Error analysis of fully discrete mixed finite element data assimilation schemes for the Navier-Stokes equations ⋮ Error analysis and iterative solvers for Navier-Stokes projection methods with standard and sparse grad-div stabilization ⋮ Approximation of coupled Stokes-Darcy flow in an axisymmetric domain ⋮ A finite element solver and energy stable coupling for 3D and 1D fluid models ⋮ On a reduced sparsity stabilization of Grad-div type for incompressible flow problems ⋮ Grad-div stabilization and subgrid pressure models for the incompressible Navier-Stokes equations ⋮ Rotational pressure-correction method for the Stokes/Darcy model based on the modular grad-div stabilization ⋮ The analogue of grad-div stabilization in DG methods for incompressible flows: limiting behavior and extension to tensor-product meshes ⋮ A decoupled, stable, and linear FEM for a phase-field model of variable density two-phase incompressible surface flow ⋮ Regularity conditions for suitable weak solutions of the Navier-Stokes system from its rotation form ⋮ Grad-div Stabilized Finite Element Schemes for the Fluid-Fluid Interaction Model ⋮ Numerical analysis of two grad-div stabilization methods for the time-dependent Stokes/Darcy model ⋮ On the convergence rate of grad-div stabilized Taylor-Hood to Scott-Vogelius solutions for incompressible flow problems ⋮ Velocity-vorticity-helicity formulation and a solver for the Navier-Stokes equations ⋮ Stabilized finite element schemes with LBB-stable elements for incompressible flows ⋮ Longer time accuracy for incompressible Navier-Stokes simulations with the EMAC formulation ⋮ Augmented Lagrangian preconditioners for the Oseen-Frank model of nematic and cholesteric liquid crystals ⋮ The effect of a sparse Grad-div stabilization on control of stationary Navier-Stokes equations ⋮ Numerical simulations of fluid pressure in the human eye ⋮ A modular Grad-div stabilization for the 2D/3D nonstationary incompressible magnetohydrodynamic equations ⋮ Uniform in Time Error Estimates for a Finite Element Method Applied to a Downscaling Data Assimilation Algorithm for the Navier--Stokes Equations ⋮ Time relaxation algorithm for flow ensembles ⋮ A second order decoupled penalty projection method based on deferred correction for MHD in Elsässer variable ⋮ Numerical analysis of a BDF2 modular grad-div stabilization method for the Navier-Stokes equations ⋮ On the accuracy of the rotation form in simulations of the Navier-Stokes equations ⋮ An efficient and modular grad-div stabilization ⋮ A Charge-Conservative Finite Element Method for Inductionless MHD Equations. Part I: Convergence ⋮ A Charge-Conservative Finite Element Method for Inductionless MHD Equations. Part II: A Robust Solver ⋮ A comparison of Cahn-Hilliard and Navier-Stokes-Cahn-Hilliard models on manifolds

Uses Software

• FEATFLOW

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Block-implicit multigrid solution of Navier-Stokes equations in primitive variables
• Multi-grid methods for Stokes and Navier-Stokes equations. Transforming smoothers: Algorithms and numerical results
• Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations
• Stabilized finite element methods. II: The incompressible Navier-Stokes equations
• An analysis of a mixed finite element method for the Navier-Stokes equations
• Additive and multiplicative multi-grid -- a comparison
• Block triangular preconditioners for nonsymmetric saddle point problems: Field-of-values analysis
• Efficient solvers for incompressible flow problems. An algorithmic and computational approach
• Stabilized spectral methods for the Navier-Stokes equations: residual-free bubbles and preconditioning
• Stabilised vs. stable mixed methods for incompressible flow
• A multigrid preconditioner for stabilised discretisations of advection-diffusion problems
• High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method
• Stabilization of incompressibility and convection through orthogonal sub-scales in finite element methods
• The convergence rate of the minimal residual method for the Stokes problem
• Anisotropic mesh refinement in stabilized Galerkin methods
• Benchmark spectral results on the lid-driven cavity flow
• On parameter choice and iterative convergence for stabilised discretisations of advection-diffusion problems
• The Stability of Mixed hp-Finite Element Methods for Stokes Flow on High Aspect Ratio Elements
• Navier--Stokes Equations in Rotation Form: A Robust Multigrid Solver for the Velocity Problem
• Stable finite-element calculation of incompressible flows using the rotation form of convection
• Bi-CGSTAB: A Fast and Smoothly Converging Variant of Bi-CG for the Solution of Nonsymmetric Linear Systems
• Preconditioning for the Steady-State Navier--Stokes Equations with Low Viscosity
• Is the steady viscous incompressible two‐dimensional flow over a backward‐facing step at Re = 800 stable?
• Effective downstream boundary conditions for incompressible Navier–Stokes equations
• Numerical performance of smoothers in coupled multigrid methods for the parallel solution of the incompressible Navier-Stokes equations
• On the domain geometry dependence of the LBB condition
• A second-order upwinding finite difference scheme for the steady Navier-Stokes equations in primitive variables in a driven cavity with a multigrid solver
• A Preconditioner for the Steady-State Navier--Stokes Equations
• Fast Nonsymmetric Iterations and Preconditioning for Navier–Stokes Equations
• Analysis of a Streamline Diffusion Finite Element Method for the Stokes and Navier–Stokes Equations
• Uzawa type algorithms for nonsymmetric saddle point problems
• ARTIFICIAL BOUNDARIES AND FLUX AND PRESSURE CONDITIONS FOR THE INCOMPRESSIBLE NAVIER-STOKES EQUATIONS
• Adaptive Galerkin finite element methods for partial differential equations
• Efficient preconditioning of the linearized Navier-Stokes equations for incompressible flow
• Geometric multigrid with applications to computational fluid dynamics

This page was built for publication: A low-order Galerkin finite element method for the Navier-Stokes equations of steady incompressible flow: a stabilization issue and iterative methods.