Conference abstracts

Session B6 - Multiresolution and Adaptivity in Numerical PDEs

July 14, 18:00 ~ 18:25

Quarklet Frames in Adaptive Numerical Schemes

Stephan Dahlke

Philipps-University of Marburg, Germany   -

This talk is concerned with the design of adaptive numerical schemes for operator equations that are based on subatomic (quarkonial) decompositions. Besides the usual space refinement, in quarkonial decompositions also a poynomial enrichment is included. We construct compactly supported, piecewise polynomial functions whose dilates and translates (quarklets) generate frames for Sobolev spaces. All frame elements except those on the coarsest level have vanishing moment properties. As a consequence, the matrix representation of elliptic operator equations in quarklet frame coordinates is compressible, which is a first important step towards the design of adaptive algorithms.

Joint work with Philipp Keding (Philipps-University of Marburg) and Thorsten Raasch (Johannes Gutenberg-University of Mainz).

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