From 1f0e3228af13e7fa685f1da9e227ee3c9318eda0 Mon Sep 17 00:00:00 2001 From: Jiaqi Zhang Date: Tue, 22 Sep 2020 20:22:49 -0400 Subject: [PATCH] update intro.dox suggested by Martin --- examples/step-74/doc/intro.dox | 14 ++++---------- 1 file changed, 4 insertions(+), 10 deletions(-) diff --git a/examples/step-74/doc/intro.dox b/examples/step-74/doc/intro.dox index 0cc4490499..fb838c6251 100644 --- a/examples/step-74/doc/intro.dox +++ b/examples/step-74/doc/intro.dox @@ -78,16 +78,10 @@ The discretization using the SIPG is given by the following weak formula

The penalty parameter

The parameter is defined as $\sigma = \gamma/h_f$, where $h_f$ a local length scale associated with the cell face, here we choose the length of the cell in the direction normal to the face, -and $\gamma$ is the penalization constant. The lower bound of $\gamma$ @cite ainsworth2007posteriori -is given by -@f[ -\gamma > 4\max_{K\in \Gamma_h}\rho\left( S_K \right). -@f] -Here $[S_K]_{i,j} = (\nu \nabla \phi_i, \nabla\phi_j)_K$. - -To ensure the discrete coercivity, the penalization constant has to be large enough. -There is no consensus in the literature on how to determine $\gamma$ in practice. One can just pick a large constant, -while other options could be the multiples of $(p+1)^2$ or $p(p+1)$. In this code, +and $\gamma$ is the penalization constant. +To ensure the discrete coercivity, the penalization constant has to be large enough @cite ainsworth2007posteriori. +People do not really have consensus on which precise formula to choose, among what was proposed in the literature. +One can just pick a large constant, while other options could be the multiples of $(p+1)^2$ or $p(p+1)$. In this code, we follow step-39 and use $\gamma = p(p+1)$.

Posteriori error estimator

-- 2.39.5