From fefe779e8b0dd3f9f25e34a3d201501f8359a8ce Mon Sep 17 00:00:00 2001 From: marcfehling Date: Sun, 24 May 2020 13:16:23 +0200 Subject: [PATCH] Apply suggestions from review Co-authored-by: Martin Kronbichler --- 9.2/paper.tex | 10 +++++----- 1 file changed, 5 insertions(+), 5 deletions(-) diff --git a/9.2/paper.tex b/9.2/paper.tex index 59ce0bf..43faf2b 100644 --- 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}. -- 2.39.5