Galerkin domain decomposition procedures for parabolic equations with three cases of boundary conditions on rectangular domain are discussed. These procedures are non‐iterative and non‐overlapping ones. They rely on implicit Galerkin method in the sub‐domains and integral mean method on the inter‐domain boundaries to present explicit flux calculation. Thus, the parallelism can be achieved by the use of these procedures. Two kinds of approximating schemes are presented. Because of the explicit nature of the flux calculation, a less severe time‐step constraint is derived to preserve stability. To bound L2‐norm error estimates, new elliptic projections are established and analyzed. Numerical experiments are provided to confirm theoretical results. Copyright © 2009 John Wiley & Sons, Ltd.