Numerical relaxation of nonconvex functionals in continuum mechanics.

To develop a fast algorithm providing a sufficiently good approximation of the quasi-convex cover is a purpose of this project (M6). The reliable and efficient numerical simulation of microstructures, as well as of time-dependent elastoplasticity problems is subject of (M8) and is treated there by means of a posteriori error control and adaptive mesh refinement in time and space. Goal-oriented and global error estimators are developed and analysed with the help of duality and energy techniques for the relaxed functional in (M7). Then the basic methodical and empiric techniques are extended to the time-dependent equation. For the time error analysis a variational formulation of the implicit Euler-time-discretisation of the energy formulation is used in (M8) which was developed by Mielke for rate-independent processes in microstructures.