From c066871b13b8de6dfb187eaff4e7cfacaf36f164 Mon Sep 17 00:00:00 2001 From: Wolfgang Bangerth Date: Wed, 8 Mar 2023 20:48:08 -0700 Subject: [PATCH] Fix a missing transpose. --- examples/step-69/doc/intro.dox | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/examples/step-69/doc/intro.dox b/examples/step-69/doc/intro.dox index edafa046b6..b6fd8d6efa 100644 --- a/examples/step-69/doc/intro.dox +++ b/examples/step-69/doc/intro.dox @@ -65,7 +65,7 @@ where $\mathbf{u}(\textbf{x},t):\mathbb{R}^{d} \times \mathbb{R} dimension. We say that $\mathbf{u} \in \mathbb{R}^{d+2}$ is the state and $\mathbb{f}(\mathbf{u}) \in \mathbb{R}^{(d+2) \times d}$ is the flux of the system. In the case of Euler's equations the state is given by -$\textbf{u} = [\rho, \textbf{m},E]^{\top}$: where $\rho \in \mathbb{R}^+$ +$\textbf{u} = [\rho, \textbf{m}^\top,E]^{\top}$: where $\rho \in \mathbb{R}^+$ denotes the density, $\textbf{m} \in \mathbb{R}^d$ is the momentum, and $E \in \mathbb{R}^+$ is the total energy of the system. The flux of the system $\mathbb{f}(\mathbf{u})$ is defined as @@ -129,7 +129,7 @@ to satisfy the constraint $\textbf{u}(\mathbf{x},t) \in \mathcal{B}$ for all $\mathbf{x} \in \Omega$ and $t \geq 0$ where @f{align} \mathcal{B} = \big\{ \textbf{u} = - [\rho, \textbf{m},E]^{\top} \in \mathbb{R}^{d+2} \, \big | + [\rho, \textbf{m}^\top,E]^{\top} \in \mathbb{R}^{d+2} \, \big | \ \rho > 0 \, , \ -- 2.39.5