A residual local projection method for the Oseen equation

A new residual local projection stabilized method (RELP) is proposed as a result of an enriched Petrov-Galerkin strategy for the Oseen problem. The PP12 × PPl pairs, l = 0, 1 with continuous or discontinuous pressures, are made stable by enhancing them with solutions of residual-based local Oseen problems and performing a static condensation procedure afterward. This process does not involve the numerical solution of the local problems and maintains the degrees of freedom of the original spaces. The method adds symmetric terms to the Galerkin formulation which are easy to implement at the element level. Consistency, well-posedness and error estimates are demonstrated, and an economic way to recover a locally conservative velocity field for the discontinuous pressure case is also proposed. Extensive numerical experiments attest the theoretical results and compare the RELP method to previously existing alternatives.