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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 flow 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. Mathematics Subject Classification (1991): 65M25

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