$\newcommand{\Dev}{\operatorname{Dev}}$ $\newcommand{\dev}{\operatorname{dev}}$ $\newcommand{\grad}{\operatorname{grad}}$ $\newcommand{\Grad}{\operatorname{Grad}}$ $\newcommand{\divg}{\operatorname{div}}$ $\newcommand{\Ei}{\operatorname{Ei}}$ $\newcommand{\tr}{\operatorname{tr}}$ $\newcommand{\Divg}{\operatorname{Div}}$ $\newcommand{\cay}{\operatorname{cay}}$ $\newcommand{\rot}{\operatorname{rot}}$

Flow resistance is typically implemented when modeling arterial flow, where the finite element domain only describes a portion of an arterial network [79]. A flow resistance may be imposed on downstream boundaries to simulate the resistance produced by the vascular network with its branches and bifurcations. The resistance is equivalent to a mean pressure which is proportional to the volumetric flow rate $Q$ , $$p=RQ\,,\quad Q=\int_{\partial\Omega}v_{n}\,da\,,$$ where $R$ is the resistance. Using the pressure-dilatation relation (5.15-5), equivalent to $p=-K\cdot e$ , this pressure may be prescribed as an essential boundary condition on the dilatation $e$ .