===affil2:
Institute for Applied Mathematics
Gottfried Wilhelm Leibniz University Hannover
===firstname:
Benjamin
===firstname4:
Alexander
===firstname3:
J\"org
===lastname2:
Starke 
===lastname:
M\"uller
===firstname5:

===affil6:

===lastname3:
Schr\"oder
===email:
bmueller@ifam.uni-hannover.de
===lastname6:

===affil5:

===otherauths:

===lastname4:
Schwarz
===affil4:
Institute of Mechanics
University of Duisburg-Essen
===lastname7:

===affil7:

===firstname7:

===postal:
Institute for Applied Mathematics
Gottfried Wilhelm Leibniz University Hannover

Welfengarten 1
D-30167 Hannover

Germany
===firstname6:

===ABSTRACT:
Elastic deformation processes play an important role in solid mechanics. In this talk, we consider nonlinear elastic behavior with a hyperelastic material law. Combined with the equations of equilibrium this forms a nonlinear first order system of partial differential equations for the displacement $u$ and the first Piola\,-\,Kirchhoff stress tensor $P$. In order to solve this system, we consider a nonlinear least squares functional, which has to be minimized. For the minimization we use the iterative Gauss\,-\,Newton method, which results in a sequence of linear least squares problems.\\
For the finite element approximation of the associated variational problem we use quadratic Raviart\,-\,Thomas elements for the stress and continuous quadratic finite elements for the displacement.
At the end of the talk we will give a numerical example and an outlook.
===affil3:
Institute of Mechanics
University of Duisburg-Essen
===lastname5:

===affilother:

===title:
Least\,-\,Squares FEM for nonlinear elasticity problems
===firstname2:
Gerhard