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The pressure formulation of the porous medium equation has been commonly used in theoretical studies due to its much better regularities than the original formulation. The goal here is to study its use in the adaptive moving mesh finite element solution. The free boundary is traced explicitly through Darcy's law. The method is shown numerically second‐order in space and first‐order in time in the pressure variable. Moreover, the convergence order of the error in the location of the free boundary is almost second‐order in the maximum norm. However, numerical results also show that the convergence order in the original variable stays between first‐order and second‐order in  L 1   norm or between 0.5th‐order and first‐order in  L 2   norm. Nevertheless, the current method can offer some advantages over numerical methods based on the original formulation for situations with large exponents or when a more accurate location of the free boundary is desired.

Adaptive finite element solution of the porous medium equation in pressure formulation