From: frohne Date: Mon, 27 Feb 2012 09:48:39 +0000 (+0000) Subject: fixing bugs X-Git-Url: https://gitweb.dealii.org/cgi-bin/gitweb.cgi?a=commitdiff_plain;h=b372d39d232c07415c849a6e92699a32b76639af;p=dealii-svn.git fixing bugs git-svn-id: https://svn.dealii.org/trunk@25174 0785d39b-7218-0410-832d-ea1e28bc413d --- diff --git a/deal.II/examples/step-41/doc/intro.dox b/deal.II/examples/step-41/doc/intro.dox index 27de519f5f..fc0f38638d 100644 --- a/deal.II/examples/step-41/doc/intro.dox +++ b/deal.II/examples/step-41/doc/intro.dox @@ -3,7 +3,8 @@ This program was contributed by Jörg Frohne (University of Siegen, Germany) while on a long-term visit to Texas A&M University.
-This material is based upon work partly supported by the ... +This material is based upon work partly supported by the ThyssenKrupp Steel Europe +company in the line with the BMBF promoted project IMAUF (www.imauf.de).
@@ -138,8 +139,8 @@ condition above.

Formulation as a saddle point problem

The variational inequality above is awkward to work with. We would therefore -like to reformulate it as an equivalent saddle point problem. Set $V:=H^1_0(\Omega)$. -We introduce a Lagrange multiplier $\lambda$ and the convex cone $K\subset V'$, $V'$ +like to reformulate it as an equivalent saddle point problem. We introduce a +Lagrange multiplier $\lambda$ and the convex cone $K\subset V'$, $V'$ dual space of $V$, $K:=\{\mu\in V': \langle\mu,v\rangle\geq 0,\quad \forall v\in V, v \le 0 \}$ of Lagrange multipliers, where $\langle\cdot,\cdot\rangle$ denotes the duality @@ -201,12 +202,10 @@ at these locations, we get a diagonal mass matrix with To define $G$ we use the same technique as for $B$. In other words, we define @f{align*} - G_{i} = \int_\Omega g_h(x) \varphi_i(\mathbf x)\ \textrm{d}x. + G_{i} = \int_\Omega g_h(x) \varphi_i(\mathbf x)\ \textrm{d}x, @f} -where $g_h$ is a -suitable approximation of $g$ and $\mathbf x_i$ is the support point of the -$i$the shape function. The integral in the definition of $B_{ii}$ and $G_i$ -are then approximated by the trapezoidal rule. +where $g_h$ is a suitable approximation of $g$. The integral in the definition +of $B_{ii}$ and $G_i$ are then approximated by the trapezoidal rule. With this, the equations above can be restated as @f{eqnarray*} &A U + B\Lambda = F,&\\ @@ -278,7 +277,7 @@ condition, we can distinguish the following cases:
Then either $[BU^k]_i\geq G_i$ and $\Lambda^k_i=0$ (no contact) or $\Lambda^k_i\geq0$ and $[BU^k]_i=G_i$ (unpressing load). -Second, the method above appears untuitively correct and useful but a bit ad +Second, the method above appears intuitively correct and useful but a bit ad hoc. However, it can be derived in a concisely in the following way. To this end, note that we'd like to solve the nonlinear system @f{eqnarray*}