The unconditional stability and mass-preservingS-DDMscheme for solving parabolic equations in three dimensions

In this paper, the unconditional stability and mass-preserving splitting domain decomposition method (S-DDM) for solving three-dimensional parabolic equations is analyzed. At each time step level, three steps (x-direction,y-direction, andz-direction) are proposed to compute the solutions on each sub-domains. The interface fluxes are first predicted by the semi-implicit flux schemes. Second, the interior solutions and fluxes are computed by the splitting implicit solution and flux coupled schemes. Last, we recompute the interface fluxes by the explicit schemes. Due to the introducedz-directional splitting and domain decomposition, the analysis of stability and convergence is scarcely evident and quite difficult. By some mathematical technique and auxiliary lemmas, we prove strictly our scheme meet unconditional stability and give the error estimates inL(2)-norm. Numerical experiments are presented to illustrate the theoretical analysis.