Abstract:In this work, we introduce semi-implicit or implicit finite difference schemes for the continuity equation with a gradient flow structure. Examples of such equations include the linear Fokker-Planck equation and the Keller-Segel equations. The two proposed schemes are first order accurate in time, explicitly solvable, and second order and fourth order accurate in space, which are obtained via finite difference implementation of the classical continuous finite element method. The fully discrete schemes are prov… Show more
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