With fourteen macro‐P2 bubbles added, a 2D P2 conforming finite element vector is constructed on quadrilateral meshes, of which the divergence is a one‐piece P1 polynomial on each quadrilateral. With a discontinuous P1 pressure space on the quadrilateral mesh, the method is shown to be stable and quasi‐optimal for solving the stationary Stokes equations. The new element produces divergence‐free velocity solutions and is pressure robust. Numerical tests show the advantages of the new divergence‐free element over the P2 Taylor‐Hood finite element.
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Hu et al. (2025) studied this question.
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