A fully discrete finite element method, based on a new weak formulation and anew time-stepping scheme, is proposed for the surface diffusion flow of closed curves in the two-dimensional plane . It is proved that the proposed method can preserve two geometric structures simultaneously at the discrete level, i.e. The perimeter of the curve decreases in time while the area enclosed by thecurve is conserved . Numerical examples are provided to demonstrate the effectiveness of the method .

Author(s) : Wei Jiang, Buyang Li

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Keywords : method - surface - discrete - perimeter - area -

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