Title: A Domain Decomposition Discretization of Parabolic Problems


Author:  Maksymilian Dryja and Xuemin Tu 

In recent years, domain decomposition methods have attracted much attention
due to their successful application to many elliptic and parabolic
problems. Domain decomposition methods treat problems based on a domain
substructuring, which is attractive for parallel computation,
due to the independence among the subdomains.   In principle, domain
decomposition methods may be applied to the system resulting from a standard
discretization of the parabolic problems or, directly, be carried out through
a direct discretization of  parabolic problems.   In this paper, a
direct domain decomposition method is introduced to discretize the parabolic
problems. The stability and convergence of this algorithm are analyzed,
and an $O(\tau+h)$ error bound is provided.