Brezzi–Douglas–Marini interpolation on anisotropic simplices and prisms

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\le p\le \infty $, and shows new estimates for anisotropic prisms with triangular base.