Stabilized spectral methods for the Navier-Stokes equations: residual-free bubbles and preconditioning

DOI10.1016/S0045-7825(98)00083-8zbMath0940.76058WikidataQ127763006 ScholiaQ127763006MaRDI QIDQ1299283

Claudio Canuto, Vincent van Kemenade, Alessandro Russo

Publication date: 19 July 2000

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

zbMATH Keywords

incompressible Navier-Stokes equationsbackward-facing stepfinite element preconditioningeigenvalues of discrete Stokes operatorregularized driven cavityresidual-free bubbles' approachstabilized spectral method

Mathematics Subject Classification ID

Navier-Stokes equations for incompressible viscous fluids (76D05) Spectral methods applied to problems in fluid mechanics (76M22)

Related Items

Streamline-upwind Petrov/Galerkin method (SUPG) vs residual-free bubbles (RFB) ⋮ Spectral semi-implicit and space-time discontinuous Galerkin methods for the incompressible Navier-Stokes equations on staggered Cartesian grids ⋮ Analytical simulation of nanoparticle-embedded blood flow control with magnetic field influence through spectra homotopy analysis method ⋮ Simulation of flows of viscoelastic fluids at high Weissenberg number using a filter-based stabilization of the spectral element method ⋮ Stabilization of the spectral element method in convection dominated flows by recovery of skew-symmetry ⋮ Variational multiscale stabilization of high-order spectral elements for the advection-diffusion equation ⋮ A review of element-based Galerkin methods for numerical weather prediction: finite elements, spectral elements, and discontinuous Galerkin ⋮ A low-order Galerkin finite element method for the Navier-Stokes equations of steady incompressible flow: a stabilization issue and iterative methods.

Cites Work

• A stable finite element for the Stokes equations
• Chebyshev pseudospectral solution of the Stokes equations using finite element preconditioning
• A relationship between stabilized finite element methods and the Galerkin method with bubble functions
• An overlapping Schwarz method for spectral element solution of the incompressible Navier-Stokes equations
• \(b=\int g\)
• Bubble-stabilized spectral methods for the incompressible Navier-Stokes equations
• Bubble stabilization of finite element methods for the linearized incompressible Navier-Stokes equations
• Krylov subspace acceleration for nonlinear multigrid schemes
• Stabilization of spectral methods by finite element bubble functions
• Bubble stabilization of spectral Legendre methods for the advection-diffusion equation
• Virtual bubbles and Galerkin-least-squares type methods (Ga.L.S.)
• Finite Element Preconditioning for Legendre Spectral Collocation Approximations to Elliptic Equations and Systems
• Conforming and nonconforming finite element methods for solving the stationary Stokes equations I
• Is the steady viscous incompressible two‐dimensional flow over a backward‐facing step at Re = 800 stable?
• CHOOSING BUBBLES FOR ADVECTION-DIFFUSION PROBLEMS
• Unsteadiness and convective instabilities in two-dimensional flow over a backward-facing step
• A POSTERIORI ERROR ESTIMATORS VIA BUBBLE FUNCTIONS