Abstract
An adaptive grid method is applied to a PDE model from geo-hydrology. Due to the higher mixed-order derivative, non-monotone waves can appear which could represent similar structures as observed in laboratory experiments [5, 16, 18]. The effectiveness of the adaptive grid, which is based on a smoothed equidistribution principle, is shown compared to uniformgrid simulations. On a uniformgrid (numerical) oscillating non-monotone wavesmay appearwhich are not present in the adaptive grid.
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