zbMATH — the first resource for mathematics

On least-squares approximations to compressible flow problems. (English) Zbl 0631.76082
A direct finite-element method for computing solutions of compressible potential flow problems is presented. An analysis of least-squares approximation is given, including optimal order estimates for piecewise polynomial approximation spaces. The model problem considered is that of potential flow past a cylinder. Numerical results for the model problem are given for a shock-free subsonic case.

76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
76M99 Basic methods in fluid mechanics
65N15 Error bounds for boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
Full Text: DOI
[1] and Elements of Gas Dynamics, John Wiley and Sons, New York, 1957.
[2] Imai, Proc. Phys. Math. Soc. Japan 23 pp 180– (1941)
[3] Hasimoto, Proc. Phys. Math. Soc. Japan 25 pp 563– (1943)
[4] Fix, Int’l. J. for Numer. Mtd. Eng. 12 pp 453– (1978)
[5] , and ”Theory ad applications of mixed finite element methods”, in Proceedings of Constructive Approaches to Mathematical Modes, A Symposium in honor of R. J. Duffin. Academic Press, New York, 1979.
[6] and An Analysis of the Finite Element Method, Prentice-Hall Inc., Englewood Cliffs, NJ, 1973.
[7] Fix, Numer. Math. 37 pp 29– (1981)
[8] Functional Analysis, Fifth Edition, Springer-Verlag, Berlin-Heidelberg, 1978. · doi:10.1007/978-3-642-96439-8
[9] Nonlinearity and Functional Analysis Academic Press, New York, 1977.
[10] and Fluid Dynamics, McGrawj-Hill Inc., New York, 1967.
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.