Elastic flow interacting with a lateral diffusion process: The one-dimensional graph case

@article{Pozzi2017ElasticFI,
  title={Elastic flow interacting with a lateral diffusion process: The one-dimensional graph case},
  author={Paola Pozzi and Bj{\"o}rn Stinner},
  journal={arXiv: Numerical Analysis},
  year={2017}
}
A finite element approach to the elastic flow of a curve coupled with a diffusion equation on the curve is analysed. Considering the graph case, the problem is weakly formulated and approximated with continuous linear finite elements, which is enabled thanks to second-order operator splitting. The error analysis builds up on previous results for the elastic flow. To obtain an error estimate for the quantity on the curve a better control of the velocity is required. For this purpose, a penalty… Expand
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