From: scott.miller <scott.miller@0785d39b-7218-0410-832d-ea1e28bc413d>
Date: Wed, 18 Sep 2013 14:28:19 +0000 (+0000)
Subject: Step-51 documentation updates.
X-Git-Url: https://gitweb.dealii.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=3f3ff9bae4d9798ddcc4a6bbd1f6d5cd384fc803;p=dealii-svn.git

Step-51 documentation updates.

git-svn-id: https://svn.dealii.org/trunk@30792 0785d39b-7218-0410-832d-ea1e28bc413d
---

diff --git a/deal.II/examples/step-51/doc/intro.dox b/deal.II/examples/step-51/doc/intro.dox
index 6679ad0a77..0badf15706 100644
--- a/deal.II/examples/step-51/doc/intro.dox
+++ b/deal.II/examples/step-51/doc/intro.dox
@@ -105,7 +105,9 @@ The HDG formulation used for this example is taken from
   <a href="http://dx.doi.org/10.1016/j.jcp.2009.01.030">[DOI]</a>
 </b>
 
-We consider the convection-diffusion equation:
+We consider the convection-diffusion equation over the domain $\Omega$
+with Dirichlet boundary $\partial \Omega_D$ and Neumann boundary
+$\partial \Omega_N$:
 @f{eqnarray*}
 	\nabla \cdot (\mathbf{c} u) - \nabla \cdot (\kappa \nabla u) &=& f,
 	\quad \text{ in } \Omega, \\
@@ -150,6 +152,9 @@ The variable $\hat {u}$ is introduced as an additional independent variable
 and is the one for which we finally set up a globally coupled linear
 system. As mentioned above, it is defined on the element faces and
 discontinuous from one face to another.
+Values for $u$ and $\mathbf{q}$ appearing in the numerical trace function
+are taken to be the cell's interior solution restricted
+to the boundary $\partial K$.  
 
 The local stabilization parameter $\tau$ has effects on stability and accuracy
 of HDG solutions; see the literature for a further discussion. A stabilization
diff --git a/deal.II/examples/step-51/doc/results.dox b/deal.II/examples/step-51/doc/results.dox
index 9f0e2bfbc0..2217fc8f37 100644
--- a/deal.II/examples/step-51/doc/results.dox
+++ b/deal.II/examples/step-51/doc/results.dox
@@ -5,7 +5,7 @@
 We first have a look at the output generated by the program when run in 2D. In
 the four images below, we show the solution for polynomial degree <i>p</i>=1
 and cycles 2, 3, 4, and 8 of the program. In the plots, we overlay the data
-generated from the internal data (DG part) with the skeleton part (lambda)
+generated from the internal data (DG part) with the skeleton part ($\hat{u}$)
 into the same plot. We had to generate two different data sets because cells
 and faces represent different geometric entities, the combination of which in
 the same file are not supported in the VTK output of deal.II.
diff --git a/deal.II/examples/step-51/step-51.cc b/deal.II/examples/step-51/step-51.cc
index ad9c58ff03..f4bb8bb265 100644
--- a/deal.II/examples/step-51/step-51.cc
+++ b/deal.II/examples/step-51/step-51.cc
@@ -361,7 +361,7 @@ namespace Step51
 
     // The 'local' solutions are interior to each element.  These
     // represent the primal solution field $u$ as well as the auxiliary
-    // field $\mathbf{q} = -\nabla u$.
+    // field $\mathbf{q}$.
     FESystem<dim>        fe_local;
     DoFHandler<dim>      dof_handler_local;
     Vector<double>       solution_local;
@@ -831,7 +831,7 @@ namespace Step51
               }
 
             // When @p trace_reconstruct=false, we are preparing assembling the
-            // system for the skeleton variable $\lambda$. If this is the case,
+            // system for the skeleton variable $\hat{u}$. If this is the case,
             // we must assemble all local matrices associated with the problem:
             // local-local, local-face, face-local, and face-face.  The
             // face-face matrix is stored as @p TaskData::cell_matrix, so that
@@ -903,7 +903,7 @@ namespace Step51
                   const unsigned int jj=scratch.fe_local_support_on_face[face][j];
                   scratch.ll_matrix(ii,jj) += tau_stab * scratch.u_phi[i] * scratch.u_phi[j] * JxW;
                 }
-
+  
             // When @p trace_reconstruct=true, we are solving for the local
             // solutions on an element by element basis.  The local
             // right-hand-side is calculated by replacing the basis functions @p
@@ -1235,7 +1235,7 @@ namespace Step51
 // the skeleton of the triangulation.  We treat it as such here, and the code is
 // similar to that above.
     DataOutFaces<dim> data_out_face(false);
-    std::vector<std::string> face_name(1,"lambda");
+    std::vector<std::string> face_name(1,"u_hat");
     std::vector<DataComponentInterpretation::DataComponentInterpretation>
     face_component_type(1, DataComponentInterpretation::component_is_scalar);