Newton's method for the Navier-Stokes equations with finite element initial guess of Stokes equations

DOI10.1016/j.camwa.2006.03.007zbMath1135.76033OpenAlexW2025318935MaRDI QIDQ2475869

Sang Dong Kim, Yong Hun Lee, Byeong Chun Shin

Publication date: 11 March 2008

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2006.03.007

zbMATH Keywords

error estimatesfinite element methodquadratic convergence

Mathematics Subject Classification ID

Navier-Stokes equations for incompressible viscous fluids (76D05) Error bounds for boundary value problems involving PDEs (65N15) Stokes and related (Oseen, etc.) flows (76D07) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Finite element methods applied to problems in fluid mechanics (76M10)

Related Items (6)

Newton's algorithm for magnetohydrodynamic equations with the initial guess from Stokes-like problem ⋮ Choice of an initial guess for Newton's method to solve nonlinear differential equations ⋮ Fractal boundaries of basin of attraction of Newton-Raphson method in helicopter trim ⋮ Newton linearization of the Navier-Stokes equations for flow computations using a fully coupled finite volume method ⋮ Resolution of the implicit Euler scheme for the Navier-Stokes equation through a least-squares method ⋮ A posteriori analysis of the Newton method applied to the Navier-Stokes problem

Cites Work

• Finite dimensional approximation of nonlinear problems. I: Branches of nonsingular solutions
• An analysis of a mixed finite element method for the Navier-Stokes equations
• On Newton-Krylov multigrid methods for the incompressible Navier-Stokes equations
• A Multigrid-Preconditioned Newton--Krylov Method for the Incompressible Navier--Stokes Equations
• Analysis of Velocity-Flux First-Order System Least-Squares Principles for the Navier--Stokes Equations: Part I
• Error estimate and regularity for the compressible Navier-Stokes equations by Newton's method
• A Multigrid Preconditioned Newton--Krylov Method

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