From bd0bb9d1b64c19d4aa5d1a0edc5bcf4a7355765d Mon Sep 17 00:00:00 2001 From: Peter Munch Date: Wed, 15 Apr 2020 22:49:24 +0200 Subject: [PATCH] Minor latex fixes in step-67 and step-69 --- examples/step-67/step-67.cc | 2 +- examples/step-69/doc/intro.dox | 10 +++++----- 2 files changed, 6 insertions(+), 6 deletions(-) diff --git a/examples/step-67/step-67.cc b/examples/step-67/step-67.cc index 85d96a9cf7..b7650612ca 100644 --- a/examples/step-67/step-67.cc +++ b/examples/step-67/step-67.cc @@ -1664,7 +1664,7 @@ namespace Euler_DG // information to cross a single cell. For information transported along with // the medium, $\mathbf u$ is scaled by the mesh size, // so an estimate of the maximal velocity can be obtained by computing - // $\|J^{-\mathrm T} \mathbf{u}\|_\inf$, where $J$ is the Jacobian of the + // $\|J^{-\mathrm T} \mathbf{u}\|_\infty$, where $J$ is the Jacobian of the // transformation from real to the reference domain. Note that // FEEvaluationBase::inverse_jacobian() returns the inverse and transpose // Jacobian, representing the metric term from real to reference diff --git a/examples/step-69/doc/intro.dox b/examples/step-69/doc/intro.dox index d2d5e44c03..9e7dd4e361 100644 --- a/examples/step-69/doc/intro.dox +++ b/examples/step-69/doc/intro.dox @@ -317,9 +317,9 @@ $t_n$: @f{align*} &\textbf{for } i \in \mathcal{V} \\ &\ \ \ \ \{\mathbf{c}_{ij}\}_{j \in \mathcal{I}(i)} \leftarrow -\texttt{gather_cij_vectors} (\textbf{c}, \mathcal{I}(i)) \\ +\texttt{gather\_cij\_vectors} (\textbf{c}, \mathcal{I}(i)) \\ &\ \ \ \ \{\textbf{U}_j^n\}_{j \in \mathcal{I}(i)} \leftarrow -\texttt{gather_state_vectors} (\textbf{U}^n, \mathcal{I}(i)) \\ +\texttt{gather\_state\_vectors} (\textbf{U}^n, \mathcal{I}(i)) \\ &\ \ \ \ \ \textbf{U}_i^{n+1} \leftarrow \mathbf{U}_i^{n} \\ &\ \ \ \ \textbf{for } j \in \mathcal{I}(i)\backslash\{i\} \\ &\ \ \ \ \ \ \ \ \texttt{compute } d_{ij} \\ @@ -327,7 +327,7 @@ $t_n$: &\ \ \ \ \ \ \ \ \textbf{U}_i^{n+1} \leftarrow \textbf{U}_i^{n+1} - \frac{\tau_n}{m_i} \mathbb{f}(\mathbf{U}_j^{n})\cdot \mathbf{c}_{ij} + d_{ij} \mathbf{U}_j^{n} \\ &\ \ \ \ \textbf{end} \\ -&\ \ \ \ \texttt{scatter_updated_state} (\textbf{U}_i^{n+1}) \\ +&\ \ \ \ \texttt{scatter\_updated\_state} (\textbf{U}_i^{n+1}) \\ &\textbf{end} @f} @@ -336,8 +336,8 @@ We note here that: - Here $\textbf{c}$ and $\textbf{U}^n$ are a global matrix and a global vector containing all the vectors $\mathbf{c}_{ij}$ and all the states $\mathbf{U}_j^n$ respectively. -- $\texttt{gather_cij_vectors}$, $\texttt{gather_state_vectors}$, and -$\texttt{scatter_updated_state}$ are hypothetical implementations that +- $\texttt{gather\_cij\_vectors}$, $\texttt{gather\_state\_vectors}$, and +$\texttt{scatter\_updated\_state}$ are hypothetical implementations that either collect (from) or write (into) global matrices and vectors. - If we assume a Cartesian mesh in two space dimensions, first-order polynomial space $\mathbb{Q}^1$, and that -- 2.39.5