Summary.
In this work we propose a numerical approach to solve some kind of degenerate parabolic equations. The underlying idea is based on the maximum principle. More precisely, we locally perturb the (initial and boundary) data instead of the nonlinear diffusion coefficients, so that the resulting problem is not degenerate. The efficiency of this method is shown analytically as well as numerically. The numerical experiments show that this new approach is comparable with the existing ones.
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Received January 20, 1999 / Revised version received February 28, 2000 / Published online July 25, 2001
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Pop, I., Yong, WA. A numerical approach to degenerate parabolic equations. Numer. Math. 92, 357–381 (2002). https://doi.org/10.1007/s002110100330
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DOI: https://doi.org/10.1007/s002110100330