From fcff49b62acaf1af22635d3d405071b1ec2856b3 Mon Sep 17 00:00:00 2001 From: Wolfgang Bangerth Date: Sat, 16 Dec 2017 08:43:26 -0700 Subject: [PATCH] Some grammar improvements. --- doc/doxygen/headers/manifold.h | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/doc/doxygen/headers/manifold.h b/doc/doxygen/headers/manifold.h index a08a7804cc..e4bd55b894 100644 --- a/doc/doxygen/headers/manifold.h +++ b/doc/doxygen/headers/manifold.h @@ -346,18 +346,18 @@ * weights have been verified to yield optimal convergence rates $\mathcal * O(h^{k+1})$ also for very high polynomial degrees, say $k=10$. * - * In literature, also other boundary descriptions are used. Before + * In the literature, other boundary descriptions are also used. Before * version 9.0 deal.II used something called Laplace smoothing where the * weights that are applied to the nodes on the circumference to get the * position of the interior nodes are determined by solving a Laplace equation - * on the unit element. However, this lead to boundary layers close to the + * on the unit element. However, this led to boundary layers close to the * curved description, i.e., singularities in the higher derivatives of the * mapping from unit to real cell. * * If the transition from a curved boundary description to a straight * description in the interior is done wrong, it is typically impossible to * achieve high order convergence rates. For example, the Laplace smoothing - * inside a single layer lead to a singularity in the fourth derivative of the + * inside a single layer leads to a singularity in the fourth derivative of the * mapping from the reference to the real cell, limiting the convergence rate * to 3 in the cells at the boundary (and 3.5 if global L2 errors were * measured in 2D). Other more crude strategies, like completely ignoring the -- 2.39.5