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.

References in corpus (2)

• Brezzi-Douglas-Marini interpolation of any order on anisotropic triangles and tetrahedra
• Pressure-robust error estimate of optimal order for the Stokes equations on domains with edges