From: Marc Fehling <marc.fehling@gmx.net>
Date: Thu, 28 May 2020 18:02:48 +0000 (+0200)
Subject: Added additional sentence describing the hp-interface.
X-Git-Url: https://gitweb.dealii.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=refs%2Fpull%2F49%2Fhead;p=release-papers.git

Added additional sentence describing the hp-interface.

Format code in listing.
---

diff --git a/9.2/paper.tex b/9.2/paper.tex
index bdcb88d..c61ab85 100644
--- a/9.2/paper.tex
+++ b/9.2/paper.tex
@@ -519,20 +519,22 @@ Consider the following (incomplete) listing as an example: We estimate both erro
 smoothness of the finite element approximation. Further, we flag certain fractions of
 cells with the highest and lowest errors for refinement and coarsening, respectively
 (here: 30\%/3\%). From those cells listed for adaptation, we designate a subset
-for $h$- and $p$-adaptation (here: 10\%/90\%).
+for $h$- and $p$-adaptation (here: 10\%/90\%). The parameters of the corresponding
+\texttt{hp::Refinement} function specify the fraction of cells to be $p$-adapted from
+those subsets flagged for refinement and coarsening, respectively.
 \begin{c++}
-Vector<float> estimated_error_per_cell (n_active_cells);
+Vector<float> estimated_error_per_cell(n_active_cells);
 KellyErrorEstimator::estimate(
   dof_handler, ..., solution, estimated_error_per_cell, ...);
 GridRefinement::refine_and_coarsen_fixed_number(
   triangulation, estimated_error_per_cell, 0.3, 0.03);
 
-Vector<float> estimated_smoothness_per_cell (n_active_cells);
+Vector<float> estimated_smoothness_per_cell(n_active_cells);
 SmoothnessEstimator::Legendre::coefficient_decay(
   ..., dof_handler, solution, estimated_smoothness_per_cell);
 hp::Refinement::p_adaptivity_fixed_number(
   dof_handler, estimated_smoothness_per_cell, 0.9, 0.9);
-hp::Refinement::choose_p_over_h (dof_handler);
+hp::Refinement::choose_p_over_h(dof_handler);
 
 triangulation.execute_coarsening_and_refinement();
 \end{c++}
@@ -542,8 +544,7 @@ smoothness estimation, and made sure that they work for refinement as well as
 coarsening in terms of $h$- and $p$-adaptation in serial and parallel applications.
 
 The former relies on knowing an estimate for the upper error bound \cite[Thm.~3.4]{BabuskaSuri1990}.
-For successive refinements, we can predict how the error will change
-based on
+For successive refinements, we can predict how the error will change based on
 current error estimates and adaptation flags. In the next refinement cycle, these
 predicted error estimates allow us to decide whether the choice of adaptation in
 the previous cycle was justified, and provide a criterion for the choice in the next