Inf-Sup Stable Non-Conforming Finite Elements on Tetrahedra With Second- and Third-Order Accuracy

Loïc Balazi; Grégoire Allaire; Pierre Jolivet; Pascal Omnes

doi:10.1002/num.70057

Inf-Sup Stable Non-Conforming Finite Elements on Tetrahedra With Second- and Third-Order Accuracy

Loïc Balazi
, Grégoire Allaire
, Pierre Jolivet
, Pascal Omnes

Research output: Contribution to journal › Article › peer-review

Abstract

We introduce a family of scalar non-conforming finite elements with second- and third-order accuracy with respect to the (Formula presented.) -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.

Original language	English
Article number	e70057
Journal	Numerical Methods for Partial Differential Equations
Volume	41
Issue number	6
DOIs	https://doi.org/10.1002/num.70057
Publication status	Published - 1 Nov 2025

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abstract = "We introduce a family of scalar non-conforming finite elements with second- and third-order accuracy with respect to the (Formula presented.) -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.",

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AU - Jolivet, Pierre

AU - Omnes, Pascal

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AB - We introduce a family of scalar non-conforming finite elements with second- and third-order accuracy with respect to the (Formula presented.) -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.

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Inf-Sup Stable Non-Conforming Finite Elements on Tetrahedra With Second- and Third-Order Accuracy

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