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

diff --git a/deal.II/examples/step-42/doc/intro.dox b/deal.II/examples/step-42/doc/intro.dox
index a7d4ab3e5b1ddab6f8ad04634c46232589261c75..5c9c2b9219ad2e71f98d4b4c370069e13227d818 100644 (file)
--- 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.