From 849f0a0f2511a879c39a9b61800df69d5849b30a Mon Sep 17 00:00:00 2001 From: bangerth Date: Wed, 13 Mar 2013 20:18:58 +0000 Subject: [PATCH] Fix missing closing brace. git-svn-id: https://svn.dealii.org/trunk@28891 0785d39b-7218-0410-832d-ea1e28bc413d --- deal.II/examples/step-42/doc/intro.dox | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) diff --git a/deal.II/examples/step-42/doc/intro.dox b/deal.II/examples/step-42/doc/intro.dox index f33e5b31fd..e968148ad2 100644 --- a/deal.II/examples/step-42/doc/intro.dox +++ b/deal.II/examples/step-42/doc/intro.dox @@ -245,7 +245,7 @@ system of equations finally. We introduce a Lagrange multiplier $\lambda$ and the convex cone $K\subset W'$, $W'$ dual space of the trace space $W:=\left[ H_0^{\frac{1}{2}}(\Gamma_C) -\right]^{\textrm{dim}$ of $V$ restricted to $\Gamma_C$, +\right]^{\textrm{dim}}$ of $V$ restricted to $\Gamma_C$, @f{gather*}K:=\{\mu\in W':\mu_T = 0,\quad\langle\mu n,v\rangle_{\Gamma_C}\geq 0,\quad \forall v\in H_0^{\frac{1}{2}}(\Gamma_C), v \ge 0\text{ on }\Gamma_C \}@f} of Lagrange multipliers, where $\langle\cdot,\cdot\rangle$ @@ -321,7 +321,7 @@ method for the contact. It sums up the results of the sections before and works @f{gather*}\mathcal{F}_{k+1}:=\lbrace p\in\mathcal{S}:\Lambda^k_p + c\left(\left[B^TU^k\right]_p - G_p\right) \leq 0\rbrace.@f} Projection $U^k$ so that it holds the second equation in (2) - @f{gather*}\hat U^K := P_{\mathcal{A}_{k+1}}(U^k).@f} + @f{gather*}\hat U^K := P_{\mathcal{A}_{k+1}}(U^k).@f}
  • If $\mathcal{A}_{k+1} = \mathcal{A}_k$ and $\vert F\left(U^{k}\right) \vert < \delta$ then stop, else set $k=k+1$ and go to step (1). @@ -372,7 +372,7 @@ Compared to step-41, step (1) is added but it should be clear from the sections above that we only linearize the problem. In step (2) we have to solve a linear system of equations again. And now the solution has to fulfill two stopping criteria. $\mathcal{A}_{k+1} = \mathcal{A}_k$ makes sure that the contact zones -are iterated out and the second ensures an accurate enough residual which means +are iterated out and the second ensures an accurate enough residual which means that the plastic zones are also iterated out. A similar method can also be found in Brunssen, Schmid, Schäfer, -- 2.39.5