Multiplicative Schwarz methods for parabolic problems. (Q1856060)

The author presents a multiplicative Schwarz domain decomposition method for semi-linear parabolic equations. Using the Euler backward time discretization and Garlekin approximation in the space variables, at a fixed time level, the resulting system is equivalent to an elliptic problem. Therefore, at each time level, the author applies the multiplicative Schwarz method, which is a powerful method for solving elliptic equations. The author studies how the convergence rate and the error estimate depend on the diameter of the sub-domain, the spacial mesh-size, the time step increment and the number of irerations at each time level. An error estimate is given. A numerical example shows that already one or two iterations at each time level can give good approximation.