Apply suggestions from review

Co-authored-by: Martin Kronbichler <kronbichler@lnm.mw.tum.de>

diff --git a/9.2/paper.tex b/9.2/paper.tex
index 59ce0bf6d8a4adee1c38686fc5a1f959ad975592..43faf2b7482fe900bb4d1e46186a63a74d98fff9 100644 (file)
--- a/9.2/paper.tex
+++ b/9.2/paper.tex
@@ -453,9 +453,9 @@ their application. Here, reference finite elements still had to be assigned manu
 to each cell, which may not lead to an optimal mesh and is tedious.
 
 With the current release, $hp$-adaptive finite element methods have been further
-expanded in both the range of features in terms of decision strategies and their 
-user interface, effectively making the more attractive to use. We introduced many
-new functions that automatize the general workflow for applying $hp$-decision
+expanded: New features like decision strategies have been added and the user interface
+has been overhauled, effectively making $hp$-methods more attractive to use. We introduced
+many new functions that automatize the general workflow for applying $hp$-decision
 strategies, which run on top of the previous low-level implementation for both serial
 and parallel applications.
 
@@ -496,8 +496,8 @@ one \cite{MelenkWohlmuth2001}.
 In general, $p$-refinement is favorable over $h$-refinement in smooth regions of
 the finite element approximation \cite[Thm.~3.4]{BabuskaSuri1990}. Thus, estimating
 its smoothness provides a suitable decision indicator for $hp$-adaptation. For this
-purpose, we expand the finite element approximation into a series of orthogonal
-basis functions of increasing complexity, and consider the decay of their expansion
+purpose, we express the finite element approximation in an orthogonal
+basis of increasing frequency, and consider the decay of their expansion
 coefficients as the estimation of smoothness. This has been implemented for both
 Fourier coefficients \cite{BangerthKayserHerold2007} and Legendre coefficients
 \cite{Mavriplis1994,HoustonSeniorSueli2003,HoustonSueli2005,EibnerMelenk2007}.