(untitled) (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 finite element, combined with the discontinuous P_1 finite element on general tetrahedral grids, is inf-sup stable for solving the Stokes equations. Consequently, such a mixed finite element method produces optimal-order convergent solutions for solving the stationary Stokes equations. Numerical tests confirm the theory.