Abstract. In this paper, we review the development of the so-called local discontinuous Galerkin method for linear incompressible
uid
ow. This is a stable, high-order accurate and locally conservative nite element method whose approximate solution is discontinuous across inter-element boundaries; this property renders the method ideally suited for hp-adaptivity. In the context of the Oseen problem, we present the method and discuss its stability and convergence properties. We also display numerical experiments that show that the method behaves well for a wide range of Reynolds numbers. 1.
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