From 4aef4a07a258779c0a985d7890bb19e2504ac89e Mon Sep 17 00:00:00 2001
From: frohne <frohne@0785d39b-7218-0410-832d-ea1e28bc413d>
Date: Mon, 28 Oct 2013 15:32:13 +0000
Subject: [PATCH] fix a bug in linearized inequality and the residual in
 overall algorithm

git-svn-id: https://svn.dealii.org/trunk@31467 0785d39b-7218-0410-832d-ea1e28bc413d
---
 deal.II/examples/step-42/doc/intro.dox | 13 ++++++++-----
 1 file changed, 8 insertions(+), 5 deletions(-)

diff --git a/deal.II/examples/step-42/doc/intro.dox b/deal.II/examples/step-42/doc/intro.dox
index a7d4ab3e5b..5c9c2b9219 100644
--- a/deal.II/examples/step-42/doc/intro.dox
+++ b/deal.II/examples/step-42/doc/intro.dox
@@ -198,9 +198,9 @@ the following equation (still an inequality, but linearized):
   \label{eq:linearization}
   \left(I_{\Pi}\varepsilon(\tilde {\mathbf u}^{i}),
     \varepsilon(\varphi) - \varepsilon(\tilde {\mathbf u}^{i})\right) \geq
-  \left(\left(I_{\Pi}\varepsilon(\tilde {\mathbf u}^{i-1}),
+  \left(\left(I_{\Pi}\varepsilon({\mathbf u}^{i-1}),
     \varepsilon(\varphi) - \varepsilon(\tilde {\mathbf u}^{i})\right) -
-  \left(P_{\Pi}(C\varepsilon(\tilde {\mathbf u}^{i-1})),
+  \left(P_{\Pi}(C\varepsilon({\mathbf u}^{i-1})),
     \varepsilon(\varphi) - \varepsilon(\tilde {\mathbf u}^{i})\right)\right),
   \quad \forall \varphi\in V^+,
 @f}
@@ -302,8 +302,11 @@ method for the contact. It works as follows:
  (1-\alpha^i_l)U^{i-1}@f}
  satisfies
  @f{gather*}
-   \vert F\left(U^{i}\right) \vert < \vert F\left(U^{i-1}\right) \vert.
+   \vert {\hat R}\left({\mathbf u}^{i}\right) \vert < \vert {\hat R}\left({\mathbf u}^{i-1}\right) \vert.
  \f}
+ with ${\hat R}\left({\mathbf u}\right)=\left(P_{Pi}(C\varepsilon(u)),\varepsilon(\varphi^{i}_p\right)$ with
+ the exceptions of (i) elements $p\in\mathcal{A}_i$ where we set ${\hat R}\left({\mathbf u}\right)=0$,
+ and (ii) elements that correpond to hanging nodes, which we eliminate in the usual manner.
 
  <li> Define the new active and inactive sets by
  @f{gather*}\mathcal{A}_{i+1}:=\lbrace p\in\mathcal{S}:\Lambda^i_p +
@@ -324,8 +327,8 @@ method for the contact. It works as follows:
  where $g_{h,p}$ is the <i>gap</i> denoting the distance of the obstacle
  from the undisplaced configuration of the body.
 
- <li> If $\mathcal{A}_{i+1} = \mathcal{A}_k$ and $\vert
- F\left(U^{i}\right) \vert < \delta$ then stop, else set $i=i+1$ and go to
+ <li> If $\mathcal{A}_{i+1} = \mathcal{A}_k$ and $\left\|
+ {\hat R}\left({\mathbf u}^{i}\right)\right) \right\|_{\ell_2} < \delta$ then stop, else set $i=i+1$ and go to
  step (1). This step ensures that we only stop iterations if both the correct
  active set has been found and the plasticity has been iterated to sufficient
  accuracy.
-- 
2.39.5