A face-centred finite volume method for second-order elliptic problems

@article{Sevilla2017AFF,
  title={A face-centred finite volume method for second-order elliptic problems},
  author={Rub{\'e}n Sevilla and Matteo Giacomini and Antonio Huerta},
  journal={ArXiv},
  year={2017},
  volume={abs/1712.06173}
}
This work proposes a novel finite volume paradigm, the face-centred finite volume (FCFV) method. Contrary to the popular vertex (VCFV) and cell (CCFV) centred finite volume methods, the novel FCFV defines the solution on the mesh faces (edges in 2D) to construct locally-conservative numerical schemes. The idea of the FCFV method stems from a hybridisable discontinuous Galerkin (HDG) formulation with constant degree of approximation, thus inheriting the convergence properties of the classical… Expand
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