From 8b848518f0f9986e755d047b0f014233299de497 Mon Sep 17 00:00:00 2001 From: Martin Kronbichler Date: Wed, 18 Sep 2013 14:48:18 +0000 Subject: [PATCH] Explain integrals git-svn-id: https://svn.dealii.org/trunk@30795 0785d39b-7218-0410-832d-ea1e28bc413d --- deal.II/examples/step-51/doc/intro.dox | 8 ++++++++ 1 file changed, 8 insertions(+) diff --git a/deal.II/examples/step-51/doc/intro.dox b/deal.II/examples/step-51/doc/intro.dox index 0badf15706..56ead0eb28 100644 --- 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 uh is defined as the space of functions that are tensor product polynomials of degree p on each cell and discontinuous over the -- 2.39.5