507 MULTILEVEL ADDITIVE METHODS FOR ELLIPTIC FINITE ELEMENT PROBLEMS M. Dryja, O. Widlund, May 1990 An additive variant of the Schwarz alternating method is discussed. A general framework is developed, which is useful in the design and analysis of a variety of domain decomposition methods as well as certain multigrid methods. Three methods of this kind are then considered and estimates of their rates of convergence given. One is a Schwarz-type method using several levels of overlapping subregions. The others use multilevel, multigrid-like decompositions of finite element spaces and have previously been considered by Yserentant and Bramble, Pasciak and Xu. Throughout, we work with finite element approximations of linear, self-adjoint, elliptic problems.