| The $MMOC$ procedure for approximating the solutions of transport-dominated diffusion problems does not automatically preserve integral conservation laws, leading to (mass) balance errors in many kinds of flows problems. The variant, called the $MMOCAA$, discussed herein preserves the conservation law at a minor additional computational cost. It is shown that its solution, in either Galerkin or finite difference form, converges at the same rates as were proved earlier by Douglas and Russell for the standard $MMOC$ procedure. Also, the application of the $MMOCAA$ to a problem in two-phase, immiscible flow in porous media is discussed. A domain decomposition procedure based on Robin transmission conditions applicable to elliptic boundary problems was first introduced by P.~L.~Loins and later discussed by a number of authors. In all of these discussions of the iterative step number. For some model problems I introduce a cycle of weights and prove that an acceleration of the convergence rate similar to that occurring for alternation-direction iteration using a cycle of pseudo-time steps results. In some discrete cases, the cycle length can be taken to be independent of the mesh spacing. I also describe an analogous procedure for a mixed finite element approximation for a model Neumann problem and to consider an overlapping subdomain of the iteration, while retaining the variable parameter cycle. It also show that a greater acceleration of the iteration can be obtained by combining overlap and the parameter cycle than by the separate use of either. |