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We propose a spectral viscosity method to approximate the two-dimensionalEuler equations with rough initial data and prove that the method converges toa weak solution for a large class of initial data, including when the initialvorticity is in the so-called Delort class i.e. it is a sum of a signed measureand an integrable function. This provides the first convergence proof for anumerical method approximating the Euler equations with such rough initial dataand closes the gap between the available existence theory and rigorousconvergence results for numerical methods. We also present numericalexperiments, including computations of vortex sheets and confined eddies, toillustrate the proposed method.

On the convergence of the spectral viscosity method for the two-dimensional incompressible Euler equations with rough initial data