On the parametric finite element approximation of evolving hypersurfaces in R3
Journal of Computational Physics
Numerical simulations of immiscible fluid clusters
Applied Numerical Mathematics
Modeling Cell Movement and Chemotaxis Using Pseudopod-Based Feedback
SIAM Journal on Scientific Computing
A Higher Order Scheme for a Tangentially Stabilized Plane Curve Shortening Flow with a Driving Force
SIAM Journal on Scientific Computing
Journal of Computational and Applied Mathematics
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We 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 and 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.