From: Wolfgang Bangerth Date: Wed, 16 May 2018 07:10:43 +0000 (+0800) Subject: Properly mark up formulas in the FE_NedelecSZ class documentation. X-Git-Tag: v9.1.0-rc1~1135^2 X-Git-Url: https://gitweb.dealii.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=a98f692beef96d528808a90fdfde7f9a8fa73f91;p=dealii.git Properly mark up formulas in the FE_NedelecSZ class documentation. --- diff --git a/include/deal.II/fe/fe_nedelec_sz.h b/include/deal.II/fe/fe_nedelec_sz.h index 96a146d3ca..bae6c46584 100644 --- a/include/deal.II/fe/fe_nedelec_sz.h +++ b/include/deal.II/fe/fe_nedelec_sz.h @@ -206,9 +206,9 @@ protected: * The main quantities which are stored are associated with edge and face * parameterisations. These are: * * * The definitions of these functionals, as well as the edge and face @@ -242,12 +242,12 @@ protected: * cell-dependent. * * The edge parameterisation of an edge, E, starting at vertex i and ending - * at vertex j is given by \sigma_{E} = \sigma_{i} - \sigma{j}. + * at vertex $j$ is given by $\sigma_{E} = \sigma_{i} - \sigma{j}$. * * sigma_imj_values[q][i][j] stores the value of the edge parametrisation - * connected by vertices i and j at the q-th quadrature point. + * connected by vertices $i$ and $j$ at the q-th quadrature point. * - * Note that not all of the i and j combinations result in valid edges on + * Note that not all of the $i$ and $j$ combinations result in valid edges on * the hexahedral cell, but they are computed in this fashion for use with * non-standard edge and face orientations. */ @@ -259,11 +259,11 @@ protected: * DoFs, which are cell-dependent. Note that the components of the gradient * are constant. * - * The edge parameterisation of an edge, E, starting at vertex i and ending - * at vertex j is given by \sigma_{E} = \sigma_{i} - \sigma{j}. + * The edge parameterisation of an edge, $E$, starting at vertex $i$ and ending + * at vertex $j$ is given by $\sigma_{E} = \sigma_{i} - \sigma{j}$. * * sigma_imj_grads[i][j][d] stores the gradient of the edge parametrisation - * connected by vertices i and j in component d. + * connected by vertices $i$ and $j$ in component $d$. * * Note that the gradient of the edge parametrisation is constant on an * edge, so we do not need to store it at every quadrature point. @@ -302,14 +302,14 @@ protected: * stored for the 12 edges such that the global vertex numbering would * follow the order defined by the "standard" deal.II cell. * - * The edge extension parameter of an edge, E, starting at vertex i and - * ending at vertex j is given by \lambda_{E} = \lambda_{i} + \lambda_{j}. + * The edge extension parameter of an edge, $E$, starting at vertex $i$ and + * ending at vertex $j$ is given by $\lambda_{E} = \lambda_{i} + \lambda_{j}$. * - * Note that under this definition, the values of \lambda_{E} do not change + * Note that under this definition, the values of $\lambda_{E}$ do not change * with the orientation of the edge. * * edge_lambda_values[m][q] stores the edge extension parameter value at - * the q-th quadrature point on edge m. + * the $q$-th quadrature point on edge $m$. */ std::vector > edge_lambda_values; @@ -320,7 +320,7 @@ protected: * deal.II cell. * * edge_lambda_grads_2d[m][d] stores the gradient of the edge extension - * parameter for component d on edge m. + * parameter for component $d$ on edge $m$. */ std::vector > edge_lambda_grads_2d; @@ -331,7 +331,7 @@ protected: * "standard" deal.II cell. * * edge_lambda_grads_3d[m][q][d] stores the gradient of the edge extension - * parameter for component d at the q-th quadrature point on edge m. + * parameter for component $d$ at the $q$-th quadrature point on edge m. */ std::vector > > edge_lambda_grads_3d; @@ -342,7 +342,7 @@ protected: * "standard" deal.II cell. * * edge_lambda_gradgrads_3d[m][d1][d2] stores the 2nd derivatives of the - * edge extension parameters with respect to components d1 and d2 on edge m. + * edge extension parameters with respect to components d1 and d2 on edge $m$. */ std::vector > > edge_lambda_gradgrads_3d; @@ -353,13 +353,13 @@ protected: * * The face extension parameter of a face, F, defined by the vertices * v1, v2, v3, v4 is given by - * \lambda_{F} = \lambda_{v1} + \lambda_{v2} + \lambda_{v3} + \lambda_{v4}. + * $\lambda_{F} = \lambda_{v1} + \lambda_{v2} + \lambda_{v3} + \lambda_{v4}$. * - * Note that under this definition, the values of \lambda_{F} do not change + * Note that under this definition, the values of $\lambda_{F}$ do not change * with the orientation of the face. * * face_lambda_values[m][q] stores the face extension parameter value at - * the q-th quadrature point on face m. + * the $q$-th quadrature point on face $m$. */ std::vector > face_lambda_values; @@ -369,7 +369,7 @@ protected: * defined by the "standard" deal.II cell. * * face_lambda_grads[m][d] stores the gradient of the face extension - * parameters for component d on face m. + * parameters for component $d$ on face $m$. */ std::vector > face_lambda_grads; };