\item Various improvements for high-order elements, including a switch of
support points in \texttt{FE\_Q} and \texttt{FE\_DGQ} to Gauss--Lobatto
- support points, more stable evaluation of Legendre polynomials, and several
+ support points, stable evaluation of high-order Legendre polynomials, and several
bugfixes for high-order polynomial mappings defined through the
\texttt{MappingQ} class.
height=0.5\textwidth,
xlabel={Number of cores},
ylabel={Solver time [s]},
- x label style={at={(0.5,0.02)}},
- y label style={at={(0.05,0.5)}},
xtick={32,128,512,2048,8192,32768,147456},
xticklabels={32,128,512,2048,8192,32k,147k},
tick label style={font=\scriptsize},
\begin{tikzpicture}
\begin{loglogaxis}[
title style={at={(1,0.965)},anchor=north east,draw=black,fill=white,font=\scriptsize\bf},
- title={$256^3$ mesh, discontinuous $\mathcal Q_3$ elements},
+ title={discontinuous $\mathcal Q_3$ elements},
width=0.48\textwidth,
height=0.5\textwidth,
xlabel={Number of cores},
- x label style={at={(0.5,0.02)}},
xtick={56,224,896,3584,14336},
xticklabels={56,224,896,3584,14336},
tick label style={font=\scriptsize},
High-order Lagrange elements, both continuous \verb!FE_Q! and discontinuous
\verb!FE_DGQ! types, now use the nodal points of the Gauss--Lobatto
quadrature formula as support points, rather than the previous equidistant
-ones. For cubic polynomials and higher, the point distribution has changed and
-thus the entries in solution vectors will look different now. Note, however,
-that using the Gauss--Lobatto points as nodal points results in much more
+ones. For cubic polynomials and higher, the point distribution has thus changed and
+thus the entries in solution vectors will look different as compared to the previous version. Note, however,
+that using the Gauss--Lobatto points as nodal points results in a much more
stable interpolation, including better iteration counts in most iterative
solvers.