Merge pull request #14987 from bangerth/7

Leave a hint in step-7.

doc/doxygen/references.bib

@@ -44,6 +44,18 @@ @article{Li2019
   url =     {https://doi.org/10.1007/s10915-019-01102-1}
 }
 
+@article{KronbichlerWall2018,
+  author    = {Kronbichler, Martin and Wall, Wolfgang A.},
+  title     = {A Performance Comparison of Continuous and Discontinuous Galerkin Methods with Fast Multigrid Solvers},
+  journal   = {SIAM Journal on Scientific Computing},
+  year      = {2018},
+  volume    = {40},
+  number    = {5},
+  pages     = {A3423--A3448},
+  url       = {https://epubs.siam.org/doi/10.1137/16M110455X},
+  doi       = {10.1137/16M110455X}
+}
+
 %-------------------------------------------------------------------------------
 % Step 10
 %-------------------------------------------------------------------------------

examples/step-7/doc/results.dox

@@ -271,7 +271,7 @@ but it should not be very hard to get the program to work!
 
 <h4> Convergence Comparison </h4>
 
-Is Q1 or Q2 better? What about adaptive versus global refinement? A (somewhat
+Is $Q_1$ or $Q_2$ better? What about adaptive versus global refinement? A (somewhat
 unfair but typical) metric to compare them, is to look at the error as a
 function of the number of unknowns.
 
@@ -288,10 +288,17 @@ work than if we used global refinement. This is not a particularly
 surprising conclusion, but it's worth checking these sorts of
 assumptions in practice.
 
-Of course, a fairer comparison would be to plot runtime (switch to release
-mode first!) instead of number of unknowns on the $x$ axis. If you
-plotted run time against the number of unknowns by timing each
-refinement step (e.g., using the Timer class), you will notice that
-the linear solver is not perfect -- its run time grows faster than
-proportional to the linear system size -- and picking a better
-linear solver might be appropriate for this kind of comparison.
+Of course, a fairer comparison would be to plot runtime (switch to
+release mode first!) instead of number of unknowns on the $x$ axis. If
+you plotted run time (check out the Timer class!) against the number
+of unknowns by timing each refinement step, you will notice that the
+linear system solver we use in this program is not perfect -- its run
+time grows faster than proportional to the linear system size -- and
+picking a better linear solver might be appropriate for this kind of
+comparison.
+
+To see how a comparison of this kind could work, take a look at
+@cite KronbichlerWall2018 , and specifically Figure 5
+that illustrates the error as a function of compute time for
+a number of polynomial degrees (as well as a number of different ways
+to discretize the equation used there).