Two-level Schwarz methods for nonconforming finite elements and discontinuous coefficients

Marcus Sarkis

Courant Institute of Mathematical Sciences, 251 Mercer Street, New York, NY 10012


A two-level domain decomposition methods are developed for a simple nonconforming approximation of second order elliptic problems. A bound is established for the condition number of these iterative methods, which grows only logarithmically with the number of degrees of freedom in each subregion. This bound holds for two and three dimensions and is independent of jumps in the value of the coefficients.