From ec4d3c36d065b396797a69d5cfaf3416af429b54 Mon Sep 17 00:00:00 2001 From: kanschat Date: Sun, 28 Nov 2010 21:02:19 +0000 Subject: [PATCH] Add some info on the notational conventions for integral operators git-svn-id: https://svn.dealii.org/trunk@22868 0785d39b-7218-0410-832d-ea1e28bc413d --- .../deal.II/integrators/local_integrators.h | 29 +++++++++++++++++++ 1 file changed, 29 insertions(+) diff --git a/deal.II/include/deal.II/integrators/local_integrators.h b/deal.II/include/deal.II/integrators/local_integrators.h index f7ed4a2eb7..c2a99840a0 100644 --- a/deal.II/include/deal.II/integrators/local_integrators.h +++ b/deal.II/include/deal.II/integrators/local_integrators.h @@ -42,6 +42,35 @@ DEAL_II_NAMESPACE_OPEN * The namespace L2 contains functions for mass matrices and * L2-inner products. * + *

Notational conventions

+ * + * In most cases, the action of a function in this namespace can be + * described by a single integral. We distinguish between integrals + * over cells Z and over faces F. If an integral is + * denoted as + * @f[ + * \int_Z u \otimes v \,dx, + * @f] + * it will yield the following results, depending on the type of + * operation + * + * + * We will use regular cursive symbols $u$ for scalars and bold + * symbols $\mathbf u$ for vectors. Test functions are always v + * and trial functions are always u. Parameters are Greek and + * the face normal vectors are $\mathbf n = \mathbf n_1 = -\mathbf + * n_2$. + * *

Signature of functions

* * Functions in this namespace follow a generic signature. In the -- 2.39.5