From: Daniel Arndt Date: Mon, 1 Aug 2016 17:40:35 +0000 (+0200) Subject: Add literature to step-35 X-Git-Tag: v8.5.0-rc1~814^2 X-Git-Url: https://gitweb.dealii.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=refs%2Fpull%2F2906%2Fhead;p=dealii.git Add literature to step-35 --- diff --git a/examples/step-35/doc/intro.dox b/examples/step-35/doc/intro.dox index f5fe3d6490..3685f54be8 100644 --- a/examples/step-35/doc/intro.dox +++ b/examples/step-35/doc/intro.dox @@ -108,8 +108,7 @@ $(u^0,p^0,\phi^0=0)$ and $(u^1,p^1,\phi^1=p^1-p^0)$. Then the projection method -Without going into details, which can be found in the corresponding literature, let us remark a few things about the -projection methods that we have just described: +Without going into details, let us remark a few things about the projection methods that we have just described: +

+The standard incremental scheme and the rotational incremental scheme were first considered by van Kan in +

+and is analyzed by Guermond in + +for the case $\nu = 1$. +It turns out that this technique suffers from unphysical boundary conditions for the kinematic pressure that +lead to reduced rates of convergence. To prevent this, Timmermans et al. proposed in + +the rotational pressure-correction projection method that uses a divergence correction for the kinematic pressure. +A thorough analysis for scheme has first been performed in + +for the Stokes problem. +

+

The Fully Discrete Setting

To obtain a fully discrete setting of the method we, as always, need a variational formulation. There is one