Heterogeneous Multiscale FEM for Diffusion Problems on Rough Surfaces

@article{Abdulle2005HeterogeneousMF,
  title={Heterogeneous Multiscale FEM for Diffusion Problems on Rough Surfaces},
  author={Assyr Abdulle and Christoph Schwab},
  journal={Multiscale Modeling & Simulation},
  year={2005},
  volume={3},
  pages={195-220}
}
We present a finite element method for the numerical solution of diffusion problems on rough surfaces. The problem is transformed to an elliptic homogenization problem in a two dimensional parameter domain with a rapidly oscillating diffusion tensor and source term. The finite element method is based on the heterogeneous multiscale methods of E and Engquist [Commun. Math. Sci., 1 (2003), pp. 87–132]. For periodic surface roughness of scale ε and amplitude O(ε), the method converges at a robust… CONTINUE READING

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