On a Residual Local Projection Method for the Incompressible Navier-Stokes Equations

Abstract

This work proposes a new residual local projection stabilized finite element method for the incompressible Navier-Stokes equations. The method adds to the Galerkin formulation new fluctuation terms which are symmetric and easily computable at the element level. The method is proved to be well-posed for the linearized model using the pair of spaces P1/P1, l = 0, 1 with continuously and discontinuously pressure interpolations. Next, we establish a new hierarchical a posteriori error estimator, and introduce a cheap strategy to recover a locally mass conservative velocity field in the discontinuous pressure case, a property usually neglected in the stabilized finite element context. Several numerical tests illustrate theoretical results.