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In this paper we consider multidimensional stochastic differential equations(SDEs) with discontinuous drift and possibly degenerate diffusion coefficient.We prove an existence and uniqueness result for this class of SDEs and wepresent a numerical method that converges with strong order 1/2. Our result isthe first one that shows strong convergence for such a general class of SDEs.  The proof is based on a transformation technique that removes thediscontinuity from the drift such that the coefficients of the transformed SDEare Lipschitz continuous. Thus the Euler-Maruyama method can be applied to thistransformed SDE. The approximation can be transformed back, giving anapproximation to the solution of the original SDE.  As an illustration, we apply our result to an SDE the drift of which has adiscontinuity along the unit circle.

A Strong Order 1/2 Method for Multidimensional SDEs with Discontinuous Drift