×
Wood, Patrick A.; Barrett, John W.

Finite element approximation of a model vortex problem. (English) Zbl 0834.65124

Numer. Funct. Anal. Optimization 16, No. 1-2, 261-285 (1995).
The authors study a semilinear elliptic free boundary value problem which arises in the context of inviscid, incompressible fluid dynamics. In particular, they are interested in finite element approximations of solutions of this problem. They show existence of a non trivial, maximal branch of solutions for both the continuous, and for the approximate problem and derive some error estimates.
Reviewer: A.J.Meir (Auburn)

MSC:

65Z05 Applications to the sciences
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
76B47 Vortex flows for incompressible inviscid fluids
76M10 Finite element methods applied to problems in fluid mechanics
35J65 Nonlinear boundary value problems for linear elliptic equations
35R35 Free boundary problems for PDEs

Keywords:

vortex problem; semilinear elliptic free boundary value problem; inviscid, incompressible fluid dynamics; finite element; error estimates
Cite Review PDF
Full Text: DOI

References:

[1] Aronson D. G., J. Diff. Eq. 39 pp 378– (1981) · Zbl 0475.35059 · doi:10.1016/0022-0396(81)90065-6
[2] Barrett J. W., R.A.I.R.O. M2:.A.N. 26 pp 627– (1992)
[3] Ciarlet P. G., The Finite Element Method for Elliptic Problems (1978) · Zbl 0383.65058
[4] Ciarlet P. G., Maximum principle and uniform convergence for the finite element method 59 pp 17– (1973) · Zbl 0251.65069
[5] Conrad F., Numer. Funct. Anal. and Optimiz 9 pp 1059– (1987) · Zbl 0647.49004 · doi:10.1080/01630568708816274
[6] Crouzeix M., On Numerical Approximation in Bifurcation Theory (1990)
[7] Eydeland A., J. Comp. Phys. 78 pp 194– (1988) · Zbl 0645.76025 · doi:10.1016/0021-9991(88)90044-7
[8] Friedman A., Partial Differential Equations (1969) · Zbl 0224.35002
[9] Gilbarg D., Elliptic Partial Differential Equations of Second Order (1983) · Zbl 0562.35001 · doi:10.1007/978-3-642-61798-0
[10] Kufner A., Function Spaces · Zbl 0869.34021
[11] Nochetto, R. H. 1991.Finite element methods for parabolic free boundary problems. in Advances in Numerical Analysis, Edited by: Light, W. Vol. 1, 34–95. O.U.P.
[12] Schatz A. H., Math. Comp. 38 pp 1– (1982)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.