In this paper, we review the development of the so-called local discontinuous Galerkin method for linearized incompressible fluid flow. This is a stable, high-order accurate and locally conservative finite 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.
Bibliographical noteFunding Information:
The first author was supported in part by the National Science Foundation (Grant DMS-0107609) and by the University of Minnesota Supercomputing Institute.