Convergence rate analysis of domain decomposition methods for obstacle problems

Abstract

Convergence rate estimate is given for an overlapping domain decomposition method for obstacle problems. It is shown that the computed solution will converge monotonically to the true solution if the intial value is above the obstacle and below the true solution. Moreover, the convergence rate is of the same order as the linear elliptic problems. Numerical experiments are shown both for the additive and the multiplicative Schwarz methods. If the overlapping size is increased by a factor of 2, the iteration number is reduced by a factor of 2.