Professor Dr. Wolfgang Dahmen
RWTH Aachen
Wavelets and Adaptivity
(Joint work with A. Cohen and R. DeVore)Abstract: Adaptive discretizations form a key methodology for treating large scale numerical simulation problems derived from partial differential or singular integral equations. This talk highlights some recent developments centering upon adaptive wavelet schemes. It is shown how concepts from nonlinear or best N-term approximation in conjunction with Besov space characterizations can be used to design and analyse adaptive schemes with asymptotically optimal complexity for a wide class of (stationary) operator equations covering e.g. singular integral equations of negative order as well as indefinite problems. Optimality means here that the scheme realizes a given target accuracy at the expense of a number of degrees of freedom and proportional computational effort that is of asymptotically lowest possible growth. A key role is played by an adaptive approximate application of (conceptually) infinite matrices to finite vectors representing elements from finite dimensional trial spaces. Several theoretical and practical aspects as well as major distinctions from conventional viewpoints and their implications will be discussed. In particular, compatibility constraints such as the LBB condition do not arise. The results are illustrated by some numerical examples.
| Zeit: | Freitag, 16. Februar 2001, 14.15 Uhr |
| Ort: | FU Berlin, Arnimallee 2-6, Raum 032 im EG |