  Recently, the $\vec{H}(\operatorname{div})$-conforming finite element
families for second order elliptic problems have come more into focus, since
due to hybridization and subsequent advances in computational efficiency their
use is no longer mainly theoretical. Their property of yielding exactly
divergence-free solutions for mixed problems makes them interesting for a
variety of applications, including incompressible fluids. In this area,
boundary and interior layers are present, which demand the use of anisotropic
elements. While for the Raviart-Thomas interpolation of any order on
anisotropic tetrahedra optimal error estimates are known, this contribution
extends these results to the Brezzi-Douglas-Marini finite elements. Optimal
interpolation error estimates are proved under two different regularity
conditions on the elements, which both relax the standard minimal angle
condition. Additionally a numerical application on the Stokes equations is
presented to illustrate the findings.
