Abstract
In this paper, we consider the cascadic multigrid method for a parabolic type equation. Backward Euler approximation in time and linear finite element approximation in space are employed. A stability result is established under some conditions on the smoother. Using new and sharper estimates for the smoothers that reflect the precise dependence on the time step and the spatial mesh parameter, these conditions are verified for a number of popular smoothers. Optimal error bounds are derived for both smooth and non-smooth data. Iteration strategies guaranteeing both the optimal accuracy and the optimal complexity are presented.
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