A new projection type stabilized formulation for the coupled Stokes Darcy flow is proposed. The method is based on the same equal order mixed finite element space for both regions. Compared with usual local projection stabilization methods, we add a new projection type stabilization term and a pressure jump term, which can effectively bypass the inf sup condition. It also ensures that our technique can be applied to not only discontinous pressure space but also continuous pressure space. At last, the stability of the proposed scheme is proved, and error estimates are obtained.
