A P 2 H-Div-Nonconforming-H-Curl Finite Element for the Stokes Equations on Triangular Meshes

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Abstract The P2 BDM H-div finite element is enriched by five P 5 P_{5} divergence-free bubbles on each triangle. The resulting finite element remains H-div and is also H-curl nonconforming. Thus the new finite element combined with the discontinuous P 1 P_{1} element for pressure, is stabilizer-free and still divergence-free in solving the Stokes equations on triangular meshes. The stabilization can also be done by three, four, or six P 5 P_{5} divergence-free bubble-enrichment each triangle, shown both in theory and in computation. Numerical tests show the advantage of the divergence-free element over the P 2 P_{2} Taylor–Hood finite element.