From 1299d80ce99846afee50f0231b216b13457e620b Mon Sep 17 00:00:00 2001 From: Timo Heister Date: Thu, 16 May 2019 14:23:46 -0600 Subject: [PATCH] doxygen: use coloneq in tutorials --- examples/step-61/doc/intro.dox | 8 ++++---- examples/step-63/doc/intro.dox | 2 +- 2 files changed, 5 insertions(+), 5 deletions(-) diff --git a/examples/step-61/doc/intro.dox b/examples/step-61/doc/intro.dox index d58cd7a8c0..017883dbfd 100644 --- a/examples/step-61/doc/intro.dox +++ b/examples/step-61/doc/intro.dox @@ -102,12 +102,12 @@ formulation of the problem, for all test functions $q$, where @f{equation*} \mathcal{A}\left(p,q\right) - := \int_\Omega \left(\mathbf{K} \nabla p\right) \cdot \nabla q \;\mathrm{d}x, + \dealcoloneq \int_\Omega \left(\mathbf{K} \nabla p\right) \cdot \nabla q \;\mathrm{d}x, @f} and @f{equation*} \mathcal{F}\left(q\right) - := \int_\Omega f \, q \;\mathrm{d}x + \dealcoloneq \int_\Omega f \, q \;\mathrm{d}x - \int_{\Gamma^N} u_N q \; \mathrm{d}x. @f} Here, we have integrated by parts in the bilinear form, and we are evaluating @@ -139,13 +139,13 @@ that is only defined in cell interiors. Consequently, for all discrete test functions $q_h$, where @f{equation*} \mathcal{A}_h\left(p_h,q_h\right) - := \sum_{K \in \mathbb{T}} + \dealcoloneq \sum_{K \in \mathbb{T}} \int_K \mathbf{K} \nabla_{w,d} p_h \cdot \nabla_{w,d} q_h \;\mathrm{d}x, @f} and @f{equation*} \mathcal{F}\left(q_h\right) - := \sum_{K \in \mathbb{T}} \int_K f \, q_h^\circ \;\mathrm{d}x + \dealcoloneq \sum_{K \in \mathbb{T}} \int_K f \, q_h^\circ \;\mathrm{d}x - \sum_{\gamma \in \Gamma_h^N} \int_\gamma u_N q_h^\partial \;\mathrm{d}x, @f} The key point is that here, we have replaced the gradient $\nabla p_h$ by the diff --git a/examples/step-63/doc/intro.dox b/examples/step-63/doc/intro.dox index 04a6fb1736..59c71cf456 100644 --- a/examples/step-63/doc/intro.dox +++ b/examples/step-63/doc/intro.dox @@ -35,7 +35,7 @@ direction, and $f$ is a source. A few notes: 2. If $\varepsilon=0$ then this is the stationary advection equation solved in step-9. -3. Define the Peclet number: $\mathcal{P}\:=\|\boldsymbol{\beta}\| +3. Define the Peclet number: $\mathcal{P} \dealcoloneq \|\boldsymbol{\beta}\| \cdot L/\varepsilon$. If $\mathcal{P}>1$, we say the problem is advection-dominated, else if $\mathcal{P}<1$ we will say the problem is diffusion-dominated. Here $L$ is the length scale of the domain. -- 2.39.5