From 7a18011827dc1fec1134476c46566ebeee44713a Mon Sep 17 00:00:00 2001 From: Peter Munch Date: Thu, 23 Jun 2022 13:30:52 +0200 Subject: [PATCH] Fix some typos --- 9.4/paper.tex | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/9.4/paper.tex b/9.4/paper.tex index b901db6..2b6da9c 100644 --- a/9.4/paper.tex +++ b/9.4/paper.tex @@ -832,8 +832,8 @@ The quadrature rule is built by meshing the polyhedral region with tetrahedra, c collecting all of the rules together, giving a \texttt{Quadrature<3>} formula on the \emph{physical} element. -These utilities will be the building blocks for adding functions to the \todo{NonMatching} namespace that will assemble coupling terms like $(u,v)_{B}$,\marginpar{The $B$ and $\Omega$ here need to be streamlined with \eqref{eq:boundingbox}, right now they are the opposite} with $B$ a domain immersed in a fixed background mesh $\Omega$ and $u,v$ finite element functions on $V_h(\Omega)$, as needed, e.g., in -the context of CutFEM (see Section~\ref{sec:cut}) of Nitsche's method to weakly impose boundary conditions at an interface. The same applies to coupling terms of the form $(u,q)_B$ in formulations using Lagrange multipliers, where now $q \in Q_h(B)$, with $Q_h(B)$ the space of the multiplier variable. +These utility functions will be the building blocks for functions in the \texttt{NonMatching} namespace that will, e.g., assemble coupling terms like $(u,v)_{B}$,\todo{The $B$ and $\Omega$ here need to be streamlined with \eqref{eq:boundingbox}, right now they are the opposite} with $B$ a domain immersed in a fixed background mesh $\Omega$ and $u,v$ finite element functions on $V_h(\Omega)$, as needed, e.g., in +the context of CutFEM (see Section~\ref{sec:cut}) or Nitsche's method to weakly impose boundary conditions at an interface. The same applies to coupling terms of the form $(u,q)_B$ in formulations using Lagrange multipliers, where now $q \in Q_h(B)$, with $Q_h(B)$ the space of the multiplier variable. Note that the most relevant difference between this and the \texttt{QuadratureGenerator} in Section~\ref{sec:cut} is that the \texttt{Quadrature} objects are created directly from two overlapping grids, one spanning over $B$ and the other one over $\Omega$, and not from a level set function. -- 2.39.5