A nonconforming P2 and discontinuous P1 mixed finite element on tetrahedral grids
Abstract
A nonconforming P2 finite element is constructed by enriching the conforming P2 finite element space with seven P2 nonconforming bubble functions (out of fifteen such bubble functions on each tetrahedron). This spacial nonconforming P2 finite element, combined with the discontinuous P1 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.
Turn this paper into a lesson
ArcXiv compiles a structured reading guide from this paper's metadata: plain-English importance, contributions, prerequisite concepts, which sections to read first, flashcards, and a quiz. Grounded in the abstract, never invented.