A Locally Modified Parametric Finite Element Method for Interface Problems

@article{Frei2014ALM,
  title={A Locally Modified Parametric Finite Element Method for Interface Problems},
  author={Stefan Frei and Thomas Richter},
  journal={SIAM J. Numer. Anal.},
  year={2014},
  volume={52},
  pages={2315-2334}
}
We present a modified finite element method that is able to approximate interface problems with high accuracy. We consider interface problems where the solution is continuous; its derivatives, however, may be discontinuous across interface curves within the domain. The proposed discretization is based on a local modification of the finite element basis functions using a fixed quadrilateral mesh. Instead of moving mesh nodes, we resolve the interface locally by an adapted parametric approach… 

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