A nonconforming P2 and discontinuous P1 mixed finite element on tetrahedral grids
<|reference_start|>A nonconforming P2 and discontinuous P1 mixed finite element on tetrahedral grids: 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 convergen solutions for solving the stationary Stokes equations. Numerical tests confirm the theory.<|reference_end|>
@article{zhang2024a,
    title={A nonconforming P2 and discontinuous P1 mixed finite element on
  tetrahedral grids},
    author={Shangyou Zhang},
    journal={arXiv preprint arXiv:2408.10227},
    year={2024},
    archivePrefix={arXiv},
    eprint={2408.10227},
    primaryClass={math.NA cs.NA}
}