# Keeping it together: a phase field version of path-connectedness and its implementation

@article{Dondl2018KeepingIT, title={Keeping it together: a phase field version of path-connectedness and its implementation}, author={P. Dondl and Stephan Wojtowytsch}, journal={arXiv: Numerical Analysis}, year={2018} }

We describe the implementation of a topological constraint in finite element simulations of phase field models which ensures path-connectedness of preimages of intervals in the phase field variable. Two main applications of our method are presented. First, a discrete steepest decent of a phase field version of a bending energy with spontaneous curvature and additional surface area penalty is shown, which leads to disconnected surfaces without our topological constraint but connected surfaces… Expand

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