A convergence theory for an overlapping Schwarz algorithm using discontinuous iterates (Q1770259)

The author proposes a new type of overlapping Schwarz methods, using discontinuous iterates. The proposed algorithm allows for discontinuous iterates across the artificial interfaces. A new theory using Lagrange multipliers is developed and conditions are found for the existence of an almost uniform convergence factor for the dual variables, which implies rapid convergence factor of the primal variables, in the two overlapping subdomanin case. Numerical examples are also presented.