Beyond pressure stabilization: A low‐order local projection method for the Oseen equation

This work proposes a new local projection stabilized finite element method (LPS) for the Oseen problem. The method adds to the Galerkin formulation new fluctuation terms that are symmetric and easily computable at the element level. Proposed for the pair ℙ1/ℙl, l = 0, 1, when the pressure is continuously or discontinuously approximated, well-posedness and error optimality are proved. In addition, we introduce a cheap strategy to recover an element-wise mass conservative velocity field in the discontinuous pressure case, a property usually neglected in the stabilized finite element context. Numerics validate the theoretical results and show that the present method improves accuracy to represent boundary layers when compared with alternative approaches.

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