An Adaptive Surface Finite Element Method Based on Volume Meshes

@article{Demlow2012AnAS,
  title={An Adaptive Surface Finite Element Method Based on Volume Meshes},
  author={Alan Demlow and Maxim A. Olshanskii},
  journal={SIAM J. Numer. Anal.},
  year={2012},
  volume={50},
  pages={1624-1647}
}
In this paper we define an adaptive version of a recently introduced finite element method for numerical treatment of elliptic PDEs defined on surfaces. The method makes use of a (standard) outer volume mesh to discretize an equation on a two-dimensional surface embedded in $\mathbb{R}^3$. Extension of the equation from the surface is avoided, but the number of degrees of freedom (d.o.f.) is optimal in the sense that it is comparable to methods in which the surface is meshed directly. In… 

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