An accurate solution procedure for fluid flow with natural convection

Lenferink, H. W. J.

doi:10.1080/01630569408816586

Cited by 20 publications

(17 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Convergence results for multilevel Newton methods for the Navier-Stokes equations are Downloaded 11/21/14 to 193.0.65.67. Redistribution subject to SIAM license or copyright; see http://www.siam.org/journals/ojsa.php given for small Reynolds numbers in [16] and in Shaidurov [32], and in the nonuniqueness case in [17,18,19,22]. The use of a coarse mesh correction was recently proposed by Xu [40,41] for semilinear elliptic problems.…”

Section: Algorithm 12: Fine Mesh Newton Update With Coarse Mesh Corrmentioning

confidence: 98%

A Two-Level Method with Backtracking for the Navier--Stokes Equations

Layton¹,

Tobiska²

1998

SIAM J. Numer. Anal.

193

View full text Add to dashboard Cite

We consider a two-level method for resolving the nonlinearity in finite element approximations of the equilibrium Navier-Stokes equations. The method yields L 2 and H 1 optimal velocity approximations and an L 2 optimal pressure approximation. The two-level method involves solving one small, nonlinear coarse mesh system, one Oseen problem (hence, linear with positive definite symmetric part) on the fine mesh, and one linear correction problem on the coarse mesh. The algorithm we study produces an approximate solution with the optimal, asymptotic in h, accuracy for any fixed Reynolds number. We do not consider the behavior of the error for fixed h as Re → ∞, i.e., for flows in transition to turbulence.

show abstract

Section: Algorithm 12: Fine Mesh Newton Update With Coarse Mesh Corrmentioning

confidence: 98%

A Two-Level Method with Backtracking for the Navier--Stokes Equations

Layton¹,

Tobiska²

1998

SIAM J. Numer. Anal.

193

View full text Add to dashboard Cite

show abstract

“…The approach based on the minimization procedure (19) has to be used when local behaviour of the residual is signiÿcantly non-linear and the linearized functional minimization does not give su ciently fast residual norm reduction. Since the minimization procedure (19) takes place on a small-dimensional set W , it is only slightly more costly then the minimization procedure (20) with backtracking. There is no need in additional scaling ofp when the non-linear minimization problem (19) is solved (see Reference [7]).…”

Section: On the Non-linear Iterative Proceduresmentioning

confidence: 99%

“…For earlier L 2 -estimates for di usion and uid ow problems, see References [18][19][20]; the approach to deriving the L 2 -estimates was also mentioned in Reference [7].…”

Section: On the Two-level Newton Proceduresmentioning

confidence: 99%

On a two-level Newton-type procedure applied for solving non-linear elasticity problems

Axelsson

Padiy

2000

Int. J. Numer. Meth. Engng.

View full text Add to dashboard Cite

The present work is devoted to the damped Newton method applied for solving a class of non‐linear elasticity problems. Following the approach suggested in earlier related publications, we consider a two‐level procedure which involves (i) solving the non‐linear problem on a coarse mesh, (ii) interpolating the coarse‐mesh solution to the fine mesh, (iii) performing non‐linear iterations on the fine mesh. Numerical experiments suggest that in the case when one is interested in the minimization of the L2‐norm of the error rather than in the minimization of the residual norm the coarse‐mesh solution gives sufficiently accurate approximation to the displacement field on the fine mesh, and only a few (or even just one) of the costly non‐linear iterations on the fine mesh are needed to achieve an acceptable accuracy of the solution (the accuracy which is of the same order as the accuracy of the Galerkin solution on the fine mesh). Copyright © 2000 John Wiley & Sons, Ltd.

show abstract

“…The a priori convergence analysis of these types of methods was pioneered by Xu [ I , 21 for semilinear elliptic problems and are related to the so-called projective Newton method . The two-level discretization methods have recently been extended to, and analyzed, for the Navier-Stokes equations in [6-81, as well as for natural convection problems [9], magneto-hydrodynamic models [lo], multiparameter continuation problems [ 1 I], and (suitably adapted) higher Reynolds flow problems [ 12, 131. The obvious computational attractions of these methods, as well as their sound theoretical support strongly suggest that they be incorporated into self-adaptive finite element algorithms. Since the two-level methodology is a distinct discretization procedure, this requires that a posteriori error estimates be developed as a basis for local error indicators: the main result of this report stated in Theorem 3.…”

Section: Introductionmentioning

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.

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

An accurate solution procedure for fluid flow with natural convection

Cited by 20 publications

References 7 publications

A Two-Level Method with Backtracking for the Navier--Stokes Equations

A Two-Level Method with Backtracking for the Navier--Stokes Equations

On a two-level Newton-type procedure applied for solving non-linear elasticity problems

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

Contact Info

Product

Resources

About