Abstract
Abstract In this paper we consider the solution of nonlinear problems in Fluid Dynamics by least square formulations and conjugate gradient algorithms. We discuss first the solution by these methods of a fairly academic example and then their applications to the transonic potential flows of compressible, inviscid fluids and to the Navier-Stokes equations of incompressible viscous fluids. The solution of the corresponding discrete problems (via finite element approximation) will be reported in forthcoming papers containing numerical examples.
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