Brezzi--Douglas--Marini interpolation on anisotropic simplices and prisms

TL;DR

This paper extends error estimates for Brezzi--Douglas--Marini interpolation to anisotropic simplices and prisms across all L^p norms, broadening the understanding of finite element approximation in anisotropic meshes.

Contribution

It provides generalized error estimates for anisotropic simplices in L^p norms and introduces new estimates for anisotropic prisms with triangular bases.

Findings

Generalized error estimates for anisotropic simplices in L^p norms (1≤p≤∞)

New estimates for anisotropic prisms with triangular bases

Enhanced understanding of interpolation errors in anisotropic finite element meshes

Abstract

The Brezzi--Douglas--Marini interpolation error on anisotropic elements has been analyzed in two recent publications, the first focusing on simplices with estimates in $L^2$, the other considering parallelotopes with estimates in terms of $L^p$-norms. This contribution provides generalized estimates for anisotropic simplices for the $L^p$ case, $1\leq p\leq\infty$, and shows new estimates for anisotropic prisms with triangular base.