A Nonconforming P2 and Discontinuous P1 Mixed Finite Element on Tetrahedral Grids (Advances in Applied Mathematics and Mechanics, 2025)
A nonconforming $P_2$ finite element is constructed by enriching the conforming $P_2$ finite element space with seven $P_2$ nonconforming bubble functions (out of fifteen such bubble functions on each tetrahedron). This spacial nonconforming $P_2$ finiteelement, combined with the discontinuous $P_1$ finite element on general tetrahedralgrids, is inf-sup stable for solving the Stokes equations. Consequently, such a mixedfinite element method produces optimal-order convergent solutions for solving thestationary Stokes equations. Numerical tests confirm the theory.