We present results obtained within the project 'Adaptive Wavelet Methods for SPDEs'. After a short overview over the goals and achievements of this project, we discuss one topic in detail: The analysis of the regularity of SPDEs, using special scales of Besov spaces to measure the regularity of the solution with respect to the space variable. The regularity in these Besov spaces determines the convergence rate of adaptive wavelet methods. Our investigations are needed in order to underpin the use of spatially adaptive wavelet methods instead of classical uniform alternatives.
This is joint work with: Stephan Dahlke (Marburg), Nicolas D÷hring (Kaiserslautern), Kyeong-Hun Kim (Seoul), Stefan Kinzel (Marburg), Kijung Lee (Suwon), Felix Lindner (Kaiserslautern), Thorsten Raasch (Mainz), Klaus Ritter (Kaiserslautern), and RenÚ L. Schilling (Dresden).