From 355f7e61784fc5ea2a847d1909429778b6710d92 Mon Sep 17 00:00:00 2001 From: Praveen C Date: Thu, 14 Dec 2017 11:18:19 +0530 Subject: [PATCH] Fix documentation In FE_RaviartThomas, the cell quadrature is wrt QGauss(k+1). Fix some mistakes in mapping, everything on right side is wrt \hat{x}. --- include/deal.II/fe/fe_raviart_thomas.h | 2 +- include/deal.II/fe/mapping.h | 15 +++++++-------- 2 files changed, 8 insertions(+), 9 deletions(-) diff --git a/include/deal.II/fe/fe_raviart_thomas.h b/include/deal.II/fe/fe_raviart_thomas.h index f44c0d8c85..9404ae2c30 100644 --- a/include/deal.II/fe/fe_raviart_thomas.h +++ b/include/deal.II/fe/fe_raviart_thomas.h @@ -93,7 +93,7 @@ DEAL_II_NAMESPACE_OPEN * quadrature rules themselves. The generalized support points are a set of * points such that this quadrature can be performed with sufficient accuracy. * The points needed are those of QGaussk+1 on each face as well as - * QGaussk in the interior of the cell (or none for + * QGaussk+1 in the interior of the cell (or none for * RT0). * * diff --git a/include/deal.II/fe/mapping.h b/include/deal.II/fe/mapping.h index 381b3c4558..73dc1ac370 100644 --- a/include/deal.II/fe/mapping.h +++ b/include/deal.II/fe/mapping.h @@ -920,8 +920,8 @@ public: * cell is also represented by a vector field, but again transforms * differently, namely by the Piola transform * @f[ - * \mathbf u(\mathbf x) = \frac{1}{\text{det}\;J(\mathbf x)} - * J(\mathbf x) \hat{\mathbf u}(\mathbf x). + * \mathbf u(\mathbf x) = \frac{1}{\text{det}\;J(\hat{\mathbf x})} + * J(\hat{\mathbf x}) \hat{\mathbf u}(\hat{\mathbf x}). * @f] * * @@ -1021,11 +1021,10 @@ public: * J(\hat{\mathbf x})^{-1}. * @f] *
  • @p mapping_piola_gradient: it assumes $\mathbf u(\mathbf x) = - * \frac{1}{\text{det}\;J(\mathbf x)} J(\mathbf x) \hat{\mathbf u}(\mathbf - * x)$ so that + * \frac{1}{\text{det}\;J(\hat{\mathbf x})} J(\hat{\mathbf x}) \hat{\mathbf u}(\hat{\mathbf x})$ so that * @f[ * \mathbf T(\mathbf x) = - * \frac{1}{\text{det}\;J(\mathbf x)} + * \frac{1}{\text{det}\;J(\hat{\mathbf x})} * J(\hat{\mathbf x}) \hat{\mathbf T}(\hat{\mathbf x}) * J(\hat{\mathbf x})^{-1}. * @f] @@ -1128,11 +1127,11 @@ public: * J_{jJ}(\hat{\mathbf x})^{-1} J_{kK}(\hat{\mathbf x})^{-1}. * @f] *
  • @p mapping_piola_hessian: it assumes $\mathbf u_i(\mathbf x) = - * \frac{1}{\text{det}\;J(\mathbf x)} J_{iI}(\mathbf x) \hat{\mathbf - * u}(\mathbf x)$ so that + * \frac{1}{\text{det}\;J(\hat{\mathbf x})} J_{iI}(\hat{\mathbf x}) \hat{\mathbf + * u}(\hat{\mathbf x})$ so that * @f[ * \mathbf T_{ijk}(\mathbf x) = - * \frac{1}{\text{det}\;J(\mathbf x)} + * \frac{1}{\text{det}\;J(\hat{\mathbf x})} * J_{iI}(\hat{\mathbf x}) \hat{\mathbf T}_{IJK}(\hat{\mathbf x}) * J_{jJ}(\hat{\mathbf x})^{-1} J_{kK}(\hat{\mathbf x})^{-1}. * @f] -- 2.39.5