Fix some typos in step-16.

Thanks to @kostyfisik for pointing out the 'that that' typo, which
prompted me to fix some other small ones.

diff --git a/examples/step-16/doc/intro.dox b/examples/step-16/doc/intro.dox
index c14a03961ed3314de5c482ff74da6369ee02f5a9..2622eefd3793fefabf2d70d536dfa67475a55aae 100644 (file)
--- a/examples/step-16/doc/intro.dox
+++ b/examples/step-16/doc/intro.dox
@@ -53,7 +53,7 @@ degrees of freedom that are defined on the refined cells, but does not
 extend to that part of the domain that is not refined. While this
 guarantees that the overall effort grows as ${\cal O}(N)$ as necessary
 for optimal multigrid complexity, it leads to problems when defining
-where to smoothen and what boundary conditions to pose for the operators
+where to smooth and what boundary conditions to pose for the operators
 defined on individual levels if the level boundary is not an external
 boundary. These questions are discussed in detail in the article cited above.
 

diff --git a/examples/step-16/doc/results.dox b/examples/step-16/doc/results.dox
index 9d2201d5b6ab1e3ead4f4d5c03a1e95212160c38..3de588e1c5186220c86fbfb80ea1991ee23d32ef 100644 (file)
--- a/examples/step-16/doc/results.dox
+++ b/examples/step-16/doc/results.dox
@@ -6,7 +6,7 @@ On the finest mesh, the solution looks like this:
   <img src="http://www.dealii.org/images/steps/developer/step-16.solution.png" alt="">
 </p>
 
-More impoartantly, we would like to see if the multigrid method really
+More importantly, we would like to see if the multigrid method really
 improved the solver performance. Therefore, here is the textual
 output:
 
@@ -64,7 +64,7 @@ it shows the power of multigrid methods.
 We encourage you to switch on timing output by calling the function
 LogStream::log_execution_time() of the deallog object and compare to
 step 6. You will see that the multigrid method has quite an overhead
-on coarse meshes, but that that it always beats other methods on fine
+on coarse meshes, but that it always beats other methods on fine
 meshes because of its optimal complexity.
 
 A close inspection of this program's performance shows that it is mostly

diff --git a/examples/step-16/step-16.cc b/examples/step-16/step-16.cc
index ced76104e65461dd62ceb5aa46bc5dd1d04184fd..d7bc1e474ec3419f53f3f3c5c749990d501cd5c9 100644 (file)
--- a/examples/step-16/step-16.cc
+++ b/examples/step-16/step-16.cc
@@ -423,7 +423,7 @@ namespace Step16
   // MeshWorker hides most of that from us, and thus the difference
   // between this function and the previous lies only in the setup of
   // the assembler and the different iterators in the loop.
-  // Also, fixing up the matrices in the end is a little more comlicated.
+  // Also, fixing up the matrices in the end is a little more complicated.
   template <int dim>
   void LaplaceProblem<dim>::assemble_multigrid ()
   {