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ABSTRACT

Firstly we propose a series of temporal high-order parametric finite element methods to simulate curvature flows. Particularly, for those flows with multiple geometric structures, e.g., surface diffusion which decreases the area and preserves the volume, we propose a type of structure-preserving methods by incorporating two scalar Lagrange multipliers and two evolution equations involving the area and volume, respectively. These schemes can effectively preserve the structure at a fully discrete level. Extensive numerical experiments demonstrate that our methods achieve the desired temporal accuracy, as measured by the manifold distance, while simultaneously preserving the geometric structure of the surface diffusion.