From f9aa2d6589bfbd5a2e82ee0ae58ca317f41ce551 Mon Sep 17 00:00:00 2001 From: Zhuoran Wang Date: Mon, 23 Mar 2020 23:46:22 -0600 Subject: [PATCH] Introduce face notations to introduction. --- examples/step-47/doc/intro.dox | 5 ++++- 1 file changed, 4 insertions(+), 1 deletion(-) diff --git a/examples/step-47/doc/intro.dox b/examples/step-47/doc/intro.dox index 86fab3feed..d401745958 100644 --- a/examples/step-47/doc/intro.dox +++ b/examples/step-47/doc/intro.dox @@ -230,7 +230,10 @@ As mentioned, this method relies on the use of $C^0$ Lagrange finite elements where the $C^1$ continuity requirement is relaxed and has been replaced with interior penalty techniques. To derive this method, we consider a $C^0$ shape function $v_h$ which vanishes on -$\partial\Omega$. Since the higher order derivatives of $v_h$ have two +$\partial\Omega$. We introduce notation $ \mathbb{F} $ as the set of +all faces of $\mathbb{T}$, $ \mathbb{F}^b $ as the set of boundary faces, +and $ \mathbb{F}^i $ as the set of interior faces for use further down below. +Since the higher order derivatives of $v_h$ have two values on each interface $e\in \mathbb{F}$ (shared by the two cells $K_{+},K_{-} \in \mathbb{T}$), we cope with this discontinuity by defining the following single-valued functions on $e$: -- 2.39.5