using a primal-dual active set strategy and algebraic multigrid, Int. J. Numer.
Meth. Engng, 2007, 69, pp. 524-543.
+\section{Adaptive mesh refinement}
+
+Since we run our program in 3d, there is a good reason to use adaptive
+mesh refined. To make life a bit easier we are choosing the
+KellyErrorEstimator that is already implemented in deal.II. We hand the
+solution vector to it which contains the displacement $u$. As we will see in the
+results it yields a quite reasonable adaptive mesh for the contact zone.
+
\section{Implementation}
+This tutorial is essentailly a mixture of step-40 and step-41 but instead of
+PETSc we let the Trilinos library deal with parallelizing the linear algebra
+(like in step-32). Since we are trying to solve a similar problem like in
+step-41 we will use the same methods but now in parallel.
+
+Another difficulty is the handling of the different constraints from
+(the dirichlet conditons), the hanging nodes and the inequality condition that
+arises from the contact. For this purpose we create three objects of type
+ConstraintMatrix.
+
+Beside the ConstitutiveLaw class there is another new class called Input. This
+class allows us to read in an obstacle from a file. In our example the file
+'obstacle\_file.dat' containts data which describe the Chinese symbol for force.
+
\end{document}