Discrete Extension Operators for Mixed finite element spaces on locally refined meshes

TL;DR

This paper proves the existence of uniformly bounded discrete extension operators for Raviart-Thomas and Nédélec finite element spaces on locally refined tetrahedral meshes, ensuring stability in mixed finite element methods.

Contribution

It establishes the existence of bounded extension operators for specific finite element spaces on locally refined meshes, advancing the theoretical foundation of mixed finite element methods.

Findings

Existence of bounded extension operators for Raviart-Thomas and Nédélec spaces.

Applicability to locally refined tetrahedral meshes.

Enhancement of stability analysis in mixed finite element discretizations.

Abstract

The existence of uniformly bounded discrete extension operators is established for conforming Raviart-Thomas and N\'ed\'elec discretisations of $H(div)$ and $H(curl)$ on locally refined partitions of a polyhedral domain into tetrahedra.