From 89f05b181899182c2626d5c73b99f2817645e0a1 Mon Sep 17 00:00:00 2001 From: Jiaqi Zhang Date: Sat, 19 Jun 2021 08:37:45 -0400 Subject: [PATCH] step-74 description --- 9.3/paper.tex | 8 +++++++- 1 file changed, 7 insertions(+), 1 deletion(-) diff --git a/9.3/paper.tex b/9.3/paper.tex index 1b75055..f01f43d 100644 --- a/9.3/paper.tex +++ b/9.3/paper.tex @@ -1089,7 +1089,13 @@ framework in parallel. The PDE considered is the Gelfand problem $-\triangle u = or alternatively as the second derivative of an energy functional that then also yields the residual itself. -\item \texttt{step-74} SIPG for the Poisson equation \todo[inline]{TODO} +\item \texttt{step-74} implements the symmetric interior penalty Galerkin +(SIPG) method for Poisson's equation using the \texttt{FEInterfaceValues} class +in combination with \texttt{MeshWorker::mesh\_loop()}. With \texttt{FEInterfaceValues}, +we can directly obtain the jump and the average of shape functions and of the solution +across cell faces, which simplifies the assembling of face terms in DG methods especially on +adaptive meshes. + \item \texttt{step-75} demonstrates a state-of-the-art way of solving a simple Laplace problem using $hp$-adaptation and hybrid multigrid methods on machines -- 2.39.5