Domain decomposition methods for linear and semilinear elliptic stochastic partial differential equations

In this paper, we study several overlapping domain decomposition methods for the numerical solutions of some linear and semilinear elliptic stochastic partial differential equations discretized by the finite element methods. In particular, we show that the algorithms converge and the convergence rates are independent of the finite element mesh parameter, as well as the number of subdomains used in the domain decomposition.