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Vortex nucleation in a Bose-Einstein condensate subject to a stirringpotential is studied numerically using the zero-temperature, two-dimensionalGross-Pitaevskii equation. It is found that this theory is able to describe thecreation of vortices, but not the crystallization of a vortex lattice. In thecase of a rotating, slightly anisotropic harmonic potential, the numericalresults reproduce experimental findings, thereby showing that finitetemperatures are not necessary for vortex excitation below the quadrupolefrequency. In the case of a condensate subject to stirring by a narrow rotatingpotential, the process of vortex excitation is described by a classical modelthat treats the multitude of vortices created by the stirrer as a continuouslydistributed vorticity at the center of the cloud, but retains a potential flowpattern at large distances from the center.Comment: 22 pages, 7 figures. Changes after referee report: one new figure,  new refs. No conclusions altere

Vortex nucleation in Bose-Einstein condensates in time-dependent traps