DFG-Research Centre "Mathematics for key technologies - MATHEON": Numerical solution of differential equations (TP C 13)

One of the main challenges in the field of computational mathematics concerns the accurate and efficient numerical solution of nonlinear partial differential equations. In many applications, the goal of a computation is better modelled by a linear bounded functional rather than the energy or L2 norm. The aim of the research project is the development of an a posteriori error analysis of goal functionals and adaptivity for nonlinear evolution equations discretized in time and in space. Attention will focus on the analysis of the space-discretization error for convex variational problems. The known methods for spatial goal-oriented error control will be compared. This class of methods will then be extended and adapted to nonlinear variational problems with applications in elastoplasticity and relaxed microstructures. Finally, time evolution strategies will be investigated and combined with goal-oriented error control techniques developed earlier.