A Multilevel Mesh Independence Principle for the Navier–Stokes Equations

Layton, William; Lenferink, H. W. J.

doi:10.1137/0733002

Cited by 92 publications

(41 citation statements)

References 10 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Unfortunately, this theory cannot easily be applied to our setting because it requires more smoothness of the infinite-dimensional iterates than ours appear to possess. We are also unable to apply the mesh-independence-based theory developed in [18,19] because the nonlinearity for the Navier-Stokes equations treated there appears only in the lower-order terms.…”

Section: Introductionmentioning

confidence: 99%

Multilevel First-Order System Least Squares for Nonlinear Elliptic Partial Differential Equations

Codd

Manteuffel²,

McCormick³

2003

SIAM J. Numer. Anal.

View full text Add to dashboard Cite

Abstract.A fully variational approach is developed for solving nonlinear elliptic equations that enables accurate discretization and fast solution methods. The equations are converted to a first-order system that is then linearized via Newton's method. First-order system least squares (FOSLS) is used to formulate and discretize the Newton step, and the resulting matrix equation is solved using algebraic multigrid (AMG). The approach is coupled with nested iteration to provide an accurate initial guess for finer levels using coarse-level computation. A general theory is developed that confirms the usual full multigrid efficiency: accuracy comparable to the finest-level discretization is achieved at a cost proportional to the number of finest-level degrees of freedom. In a companion paper, the theory is applied to elliptic grid generation (EGG) and supported by numerical results.

show abstract

Section: Introductionmentioning

confidence: 99%

Multilevel First-Order System Least Squares for Nonlinear Elliptic Partial Differential Equations

Codd

Manteuffel²,

McCormick³

2003

SIAM J. Numer. Anal.

View full text Add to dashboard Cite

show abstract

“…The basic two-level algorithm of [6,8] now begins with a coarse mesh finite element space Y H = ( X H , Q H ) and a fine mesh finite element space Yh = ( X " , Q " ) , and computes ( u h , p h ) E Y/' as follows.…”

Section: A Posterlorl Error Analysis Of the Two-level Discretizationmentioning

confidence: 99%

A posteriori error estimators for a two-level finite element method for the Navier-Stokes equations

Ervin

Layton

Maubach

1996

Numer. Methods Partial Differential Eq.

Self Cite

View full text Add to dashboard Cite

Two-and multilevel truncated Newton finite element discretizations are presently a very promising approach for approximating the (nonlinear) Navier-Stokes equations describing the equilibrium flow of a viscous, incompressible fluid. Their combination with mesh adaptivity is considered in this article. Specifically, locally calculable c1 posteriori error estimators are derived, with full mathematical support, for the basic two-level discretization of the Navier-Stokes equations. 0 1996

show abstract

“…Apparently, the two-level method was proposed first in [16,15,14] and used for semilinear elliptic problems. The method was implemented for the velocity-pressure formulation of the Navier-Stokes equations in [11][12][13] and for the streamfunction formulation of the Navier-Stokes equations in [8,17].…”

Section: Introductionmentioning

confidence: 99%

Two Level Finite Element Technique for Pressure Recovery from Stream Function Formulation of the Navier-Stokes Equations

Fairag

2002

Lecture Notes in Computational Science and Engineering

View full text Add to dashboard Cite

Abstract. We consider two-level finite element discretization methods for the stream function formulation of the Navier-Stokes equations. The two-level method consists of solving a small nonlinear system on the coarse mesh, then solving a linear system on the fine mesh. It is shown in [8] that the errors between the coarse and fine meshes are related superlinearly. This paper presents an algorithm for pressure recovery and a general analysis of convergence for the algorithm. The numerical example for the 2D driven cavity fluid is considered. Streamfunction contours are displayed showing the main features of the flow.

show abstract

A Multilevel Mesh Independence Principle for the Navier–Stokes Equations

Cited by 92 publications

References 10 publications

Multilevel First-Order System Least Squares for Nonlinear Elliptic Partial Differential Equations

Multilevel First-Order System Least Squares for Nonlinear Elliptic Partial Differential Equations

A posteriori error estimators for a two-level finite element method for the Navier-Stokes equations

Two Level Finite Element Technique for Pressure Recovery from Stream Function Formulation of the Navier-Stokes Equations

Contact Info

Product

Resources

About