Two Multi-Level Algorithms for the Dam Problem
We describe two multi-level algorithms for the numerical solution of stationary porous flow free boundary problems. The first one calculates two convergent sequences of super — solutions and subsolutions. It combines projected relaxation steps as proposed by Alt in  with corrections of the pressure in the saturated region. This conservative correction preserves the monotonicity. In the second (heuristic) algorithm, we apply the FAS technique to the dam problem and use an approximation of the full problem on the coarse grid. Several numerical examples are presented. For large problems, the multi-level algorithms are significantly faster than previous algorithms in which only one grid is used.
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