Explain integrals

git-svn-id: https://svn.dealii.org/trunk@30795 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 0badf15706079255f5063b56d0d7da8ba497999b..56ead0eb287c051b665da35b32a9fe89adcefef5 100644 (file)
--- a/deal.II/examples/step-51/doc/intro.dox
+++ b/deal.II/examples/step-51/doc/intro.dox
@@ -211,6 +211,14 @@ The unknowns $(\mathbf{q}_h, u_h)$ are referred to as local variables; they are
 represented as standard DG variables.  The unknown $\hat{u}_h$ is the skeleton
 variable which has support on the codimension-1 surfaces (faces) of the mesh.
 
+We use the notation $(\cdot, \cdot)_{\mathcal{T}} = \sum_K (\cdot, \cdot)_K$
+to denote the sum of integrals over all cells and $\left<\cdot,
+\cdot\right>_{\partial \mathcal{T}} = \sum_K \left<\cdot,
+\cdot\right>_{\partial K}$ to denote integration over all faces of all cells,
+i.e., interior faces are visited twice. When combining the contribution from
+both elements sharing a face, the above equation yields terms familiar for DG
+with jumps of the solution over the cell boundaries.
+
 In the equation above, the space $\mathcal {W}_h^{p}$ for the scalar variable
 <i>u<sub>h</sub></i> is defined as the space of functions that are tensor
 product polynomials of degree <i>p</i> on each cell and discontinuous over the