MIXED FINITE-ELEMENT METHODS FOR INCOMPRESSIBLE-FLOW PROBLEMS

This paper presents finite-element methods to approximate both inviscid and viscous incompressible flow problems. First one introduces general ideas and a scheme is presented for inviscid flow using discontinuous finite elements which allow a precise definition of upwind derivatives. It is then shown that such a scheme can be extended to viscous flow if the viscosity terms are treated through mixed finite elements. We give numerical results that show that this approach enables to compute at fairly large Reynolds number with reasonable accuracy. A complete error analysis is up to now out of reach, but we give results on model problems to get at least an intuitive view of the quality of the method proposed. © 1979.