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. A detailed a priori error estimate is provided for a continuous-discontinuous Galerkin ?nite element method for the generalized 2D vorticity dynamics equations. These equations describe several types of geophysical ows, including the Euler equations. The algorithm consists of a continuous Galerkin ?nite element method for the stream function and a discontinous Galerkin ?nite element method for the (potential) vorticity. Since this algorithm satis?es a number of invariants, such as energy and enstrophy conservation, it is possible to provide detailed error estimates for this non-linear problem. The main result of the analysis is a reduction in the smoothness requirements on the vorticity field from $H^2(\Omega),$ obtained in a previous analysis, to $W_p^r(\Omega)$ with $r>\frac{1}{p}$ and $p>2.$ In addition, sharper estimates for the dependence of the error on time and numerical examples on a model problem are provided

Error Analysis of a Continuous-Discontinuous Galerkin Finite Element Method for Generalized 2D Vorticity Dynamics