From 6c28bb8a286299fdd6dad796f11877931fbc38d7 Mon Sep 17 00:00:00 2001 From: Guido Kanschat Date: Sat, 23 Nov 2013 21:00:20 +0000 Subject: [PATCH] Add documentation git-svn-id: https://svn.dealii.org/trunk@31778 0785d39b-7218-0410-832d-ea1e28bc413d --- deal.II/include/deal.II/integrators/laplace.h | 31 +++++++++++++++++-- 1 file changed, 28 insertions(+), 3 deletions(-) diff --git a/deal.II/include/deal.II/integrators/laplace.h b/deal.II/include/deal.II/integrators/laplace.h index fd9564c374..61a58afbb8 100644 --- a/deal.II/include/deal.II/integrators/laplace.h +++ b/deal.II/include/deal.II/integrators/laplace.h @@ -230,7 +230,9 @@ namespace LocalIntegrators * valued version, namely on the face F * the vector * @f[ - * \int_F \Bigl(\gamma (u-g) v - \partial_n u v - (u-g) \partial_n v\Bigr)\;ds. + * \int_F \Bigl(\gamma (\mathbf u- \mathbf g) \cdot \mathbf v + - \partial_n \mathbf u \cdot \mathbf v + - (\mathbf u-\mathbf g) \cdot \partial_n \mathbf v\Bigr)\;ds. * @f] * * Here, u is the finite element function whose values and @@ -349,6 +351,20 @@ namespace LocalIntegrators } } + /** + * Flux for the interior penalty method for the Laplacian applied + * to the tangential components of a vector field, namely on + * the face F the matrices associated with the bilinear form + * @f[ + * \int_F \Bigl( \gamma [u_\tau][v_\tau] - \{\nabla u_\tau\}[v_\tau\mathbf n] - [u_\tau\mathbf + * n]\{\nabla v_\tau\} \Bigr) \; ds. + * @f] + * + * @warning This function is still under development! + * + * @author Bärbel Janssen, Guido Kanschat + * @date 2013 + */ template void ip_tangential_matrix ( FullMatrix &M11, @@ -421,7 +437,11 @@ namespace LocalIntegrators } /** - * Residual term for the symmetric interior penalty method. + * Residual term for the symmetric interior penalty method: + * @f[ + * \int_F \Bigl( \gamma [u][v] - \{\nabla u\}[v\mathbf n] - [u\mathbf + * n]\{\nabla v\} \Bigr) \; ds. + * @f] * * @author Guido Kanschat * @date 2012 @@ -483,7 +503,12 @@ namespace LocalIntegrators /** - * Vector-valued residual term for the symmetric interior penalty method. + * Vector-valued residual term for the symmetric interior penalty method: + * @f[ + * \int_F \Bigl( \gamma [\mathbf u]\cdot[\mathbf v] + - \{\nabla \mathbf u\}[\mathbf v\otimes \mathbf n] + - [\mathbf u\otimes \mathbf n]\{\nabla \mathbf v\} \Bigr) \; ds. + * @f] * * @author Guido Kanschat * @date 2012 -- 2.39.5