Convergence of a Galerkin method for 2‐D discontinuous Euler flows

We prove the convergence of a discontinuous Galerkin method approximating the 2‐D incompressible Euler equations with discontinuous initial vorticity: ω₀ ϵ L²(Ω). Furthermore, when ω₀ ϵ L^∞(Ω), the whole sequence is shown to be strongly convergent. This is the first convergence result in numerical approximations of this general class of discontinuous flows. Some important flows such as vortex patches belong to this class. © 2000 John Wiley & Sons, Inc.