Bound preserving and energy dissipative schemes for porous medium equation

A class of bound preserving and energy dissipative schemes for the porous medium equation are constructed in this paper. The schemes are based on a positivity preserving approach for Wasserstein gradient flow and a perturbation technique, and are shown to be uniquely solvable, bound preserving, and in the first-order case, also energy dissipative. Ample numerical results are presented to validate the theoretical results and demonstrate the effectiveness of the new schemes.