This volume collects some of the papers presented at the Workshop on Do main Decompositionheld at ETH, Zurich, on June 7-8th 2001. The Workshop was organized by Luca F. Pavarino (University of Milan), Christoph Schwab (ETH Zurich), Andrea Toselli (ETH Zurich), and OlofB. Widlund (Courant Institute of Mathematical Sciences). Our sponsors were the University of Milan, Department of Mathematics (MURST projects: "Calcolo Scientifico: modelli e metodi numerici innovativi" and "Simmetrie, forme geometriche, evoluzione e memoria nelle equazioni alle derivate parziali"), the Seminar for Applied...