On the Divergence Constraint in Mixed Finite Element Methods for Incompressible Flows

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Global in time stability and accuracy of IMEX-FEM data assimilation schemes for Navier–Stokes equations (2018, background): “For most common element choices, grad-div stabilization is known to improve mass conservation and reduce the effect of the pressure on the velocity error [28]; a similar effect is observed in the convergence result for this DA scheme, as well as in the numerical tests.”
A discontinuous skeletal method for the viscosity-dependent Stokes problem (2015, unknown): “…the key novelty introduced in the present work is the construction of a high-order, divergence-preserving velocity reconstruction operator on simplicial meshes, whose role is to ensure an exact balance of the curl-free part of all the forces in the momentum equation [30, 25] at the discrete level.”