Prof. Dr. Angela Kunoth
Institut für Angewandte Mathematik und Institut für Numerische Simulation, Universität Bonn
Adaptive Methods for Stationary Variational Problems from a Wavelet Perspective
Abstract: For the numerical solution of large scale systems driven by (systems of) stationary PDEs, wavelets provide a new paradigm with respect to efficiency and optimal complexity. Specifically, PDE-constrained control problems require to repeatedly solve a system of PDEs for the involved variables state, costate and control. For control problems involving elliptic PDEs, I will address preconditioning issues, the selection of appropriate norms in the control functional, and the design of an adaptive method. Convergence and asymptotically optimal complexity of the algorithm when compared to wavelet-best N-term approximations of the relevant variables are shown. The results are further extended to the design of adaptive methods for goal--oriented problems where a functional of the solution of an elliptic PDE is to be computed up to arbitrary accuracy at possibly minimal cost. The theory is complemented by corresponding numerical experiments.| Zeit: | Freitag, 28. Oktober 2005, 14.15 Uhr (Kaffee/Tee um 15.30) |
| Ort: | FU Berlin, Arnimallee 2-6, Raum 032 im EG |