Inf-sup stable non-conforming finite elements on tetrahedra with second and third order accuracy

Loïc Balazi (1, 2) , Grégoire Allaire (2) , Pierre Jolivet (3) , Pascal Omnes (1, 4)

1 SGLS - Service de Génie Logiciel pour la Simulation
2 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
3 PEQUAN - Performance et Qualité des Algorithmes Numériques
4 LAGA - Laboratoire Analyse, Géométrie et Applications

We introduce a family of scalar non-conforming finite elements with second and third order accuracy with respect to the $H^1$-norm on tetrahedra. Their vector-valued versions generate, together with discontinuous pressure approximations of order one and two respectively, inf-sup stable finite element pairs with convergence order two and three for the Stokes problem in energy norm.

Domains: Mathematics [math]

Loïc Balazi, Grégoire Allaire, Pierre Jolivet, Pascal Omnes. Inf-sup stable non-conforming finite elements on tetrahedra with second and third order accuracy. 2024. ⟨hal-04541809⟩