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John. W. Barrett, Harald Garcke, Robert NurnbergOn the Variational Approximation of Combined Second and Fourth Order Geometric Evolution EquationsWe present a variational formulation of combined motion by minus the Laplacian of curvature and mean curvature flow, as well as related flows. The proposed scheme covers both the closed curve case, as well as the case of curves that are connected via triple or quadruple junction points or intersect the external boundary. On introducing a parametric finite element approximation, we prove stability bounds and compare our scheme with existing approaches. The presented scheme has very good properties with respect to the equidistribution of mesh points and, if applicable, area conservation.Bibliographical note: |