Hybridizable discontinuous Galerkin and mixed finite element methods for elliptic problems on surfaces

@article{Cockburn2016HybridizableDG,
  title={Hybridizable discontinuous Galerkin and mixed finite element methods for elliptic problems on surfaces},
  author={Bernardo Cockburn and Alan Demlow},
  journal={Math. Comput.},
  year={2016},
  volume={85},
  pages={2609-2638}
}
We define and analyze hybridizable discontinuous Galerkin methods for the Laplace-Beltrami problem on implicitly defined surfaces. We show that the methods can retain the same convergence and superconvergence properties they enjoy in the case of flat surfaces. Special attention is paid to the relative effect of approximation of the surface and that introduced by discretizing the equations. In particular, we show that when the geometry is approximated by polynomials of the same degree of those… 

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