A high order discontinuous Galerkin Nitsche method for elliptic problems with fictitious boundary

@article{Johansson2013AHO,
  title={A high order discontinuous Galerkin Nitsche method for elliptic problems with fictitious boundary},
  author={August Johansson and Mats G. Larson},
  journal={Numerische Mathematik},
  year={2013},
  volume={123},
  pages={607-628}
}
We present a discontinuous Galerkin method, based on the classical method of Nitsche, for elliptic problems with an immersed boundary representation on a structured grid. In such methods very small elements typically occur at the boundary, leading to breakdown of the discrete coercivity as well as numerical instabilities. In this work we propose a method that avoids using very small elements on the boundary by associating them to a neighboring element with a sufficiently large intersection with… CONTINUE READING
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