Numerical analysis of the Navier-Stokes equations

zbMath0798.76041MaRDI QIDQ1316584

Rolf Rannacher

Publication date: 14 March 1994

Published in: Applications of Mathematics (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/15759

zbMATH Keywords

boundary conditionsnonlinear Galerkin methodwell-posednessincompressibility constraintChorin's projection method

Mathematics Subject Classification ID

Navier-Stokes equations for incompressible viscous fluids (76D05) 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

Variational resolution of outflow boundary conditions for incompressible Navier–Stokes ⋮ On discrete projection methods for the incompressible Navier-Stokes equations: An algorithmical approach ⋮ A posteriori error estimates for the generalized Stokes problem ⋮ Basic properties of solution of the non-steady Navier-Stokes equations with mixed boundary conditions in a bounded domain ⋮ Error estimates of mixed finite element methods for time-fractional Navier-Stokes equations ⋮ Solutions to the Navier-Stokes equations with mixed boundary conditions in two-dimensional bounded domains ⋮ On the numerical simulation of the unsteady free fall of a solid in a fluid. I: The Newtonian case ⋮ Estimates of deviations from exact solutions for boundary-value problems with incompressibility condition ⋮ On the Navier-Stokes flows for heat-conducting fluids with mixed boundary conditions

Cites Work

• Unnamed Item
• Unnamed Item
• Nonlinear Galerkin methods: The finite elements case
• A new finite element formulation for computational fluid dynamics. V: Circumventing the Babuška-Brezzi condition: A stable Petrov-Galerkin formulation of the Stokes problem accommodating equal-order interpolations
• Some current CFD issues relevant to the incompressible Navier-Stokes equations
• On uniqueness questions in the theory of viscous flow
• On the theory of semi-implicit projection methods for viscous incompressible flow and its implementation via a finite element method that also introduces a nearly consistent mass matrix. Part 1: Theory
• Finite-Element Approximation of the Nonstationary Navier–Stokes Problem. Part IV: Error Analysis for Second-Order Time Discretization
• Finite Element Approximation of the Nonstationary Navier–Stokes Problem, Part II: Stability of Solutions and Error Estimates Uniform in Time
• Finite Element Approximation of the Nonstationary Navier–Stokes Problem III. Smoothing Property and Higher Order Error Estimates for Spatial Discretization
• Modelling of the interaction of small and large eddies in two dimensional turbulent flows
• 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
• On the Question of Turbulence Modeling by Approximate Inertial Manifolds and the Nonlinear Galerkin Method
• Tools for simulating non‐stationary incompressible flow via discretely divergence‐free finite element models
• On the Rate of Convergence of the Nonlinear Galerkin Methods
• Numerical Solution of the Navier-Stokes Equations
• On error estimates of some higher order penalty-projection methods for Navier-Stokes equations