Abstract
We present a strategy for solving time-dependent problems on grids with local refine- ments in time using different time steps in different regions of space. We propose two conservative approximations based on finite volume with piecewise constant projections and domain decompo- sition techniques. Next we present an iterative method for solving the composite-grid system that reduces to solution of standard problems with standard time stepping on the coarse and fine grids. At every step of the algorithm, conservativity is ensured. Finally, numerical results on parabolic and a two-phase flow problems illustrate the accuracy of the proposed methods.
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