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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.

MSC:
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
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