TY - JOUR
T1 - A Nonconforming P2 and Discontinuous P1 Mixed Finite Element on Tetrahedral Grids
AU - Zhang , Shangyou
JO - Advances in Applied Mathematics and Mechanics
VL - 4
SP - 1259
EP - 1274
PY - 2025
DA - 2025/05
SN - 17
DO - http://doi.org/10.4208/aamm.OA-2023-0316
UR - https://global-sci.org/intro/article_detail/aamm/24061.html
KW - Quadratic finite element, nonconforming finite element, mixed finite element, Stokes equations, tetrahedral grid.
AB - <p style="text-align: justify;">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.</p>