From e0ce2ae71122fdbb4aacca1c48de89e837a57831 Mon Sep 17 00:00:00 2001 From: Zhuoran Wang Date: Thu, 28 May 2020 11:40:43 -0600 Subject: [PATCH] add description for step-47. --- 9.2/paper.tex | 14 +++++++++++--- 1 file changed, 11 insertions(+), 3 deletions(-) diff --git a/9.2/paper.tex b/9.2/paper.tex index 4890e06..3e60f81 100644 --- a/9.2/paper.tex +++ b/9.2/paper.tex @@ -170,7 +170,7 @@ \author[13]{Zhuoran Wang} \affil[13]{Department of Mathematics, Colorado State University, Fort Collins, CO 80523-1874, USA. -{\texttt{zhrwang@colostate.edu}}} +{\texttt{zhrwang@math.colostate.edu}}} \renewcommand{\labelitemi}{--} @@ -732,8 +732,16 @@ all cells in this way. In addition, there are a number of new tutorial programs: \begin{itemize} -\item \texttt{step-47} -\todo[inline]{Zhuoran to write} +\item \texttt{step-47} solves the biharmonic equation with the + clamped boundary condition. This program is based on the $C^0$ interior + penalty method for fourth order problems. In order to overcome + shortcomings of classical approaches, this method uses $C^0$ Lagrange finite + elements and introduces ``jump`` and ``average`` on interfaces of elements. + The resulting system is obtained through integration by parts, symmetrization, + and stabilization. Appropriate choices for the penalty parameter are + discussed based on numerical results. + + \item \texttt{step-50} \todo[inline]{Timo/Conrad/... to write} -- 2.39.5