Continuous Interior Penalty stabilization for divergence-free finite element methods
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In this paper we propose, analyze, and test numerically a pressure-robust stabilized finite element for a linearized case of the Navier-Stokes' equation in the high Reynolds number regime, also known as Oseen's problem. Stabilization terms are defined by jumps of different combinations of derivatives for the convective term over the element faces of the triangulation of the domain. With the help of these stabilizing terms, and the fact the finite element space is assumed to provide a point-wise divergence-free velocity, an 𝒪(h^k+1/2) error estimate in the L^2-norm is proved for the method (in the convection-dominated regime), and optimal order estimates in the remaining norms of the error. Numerical results supporting the theoretical findings are provided.
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