Finite volume scheme for multi-dimensional drift-diffusion equations and convergence analysis

Claire Chainais-Hillairet Université Blaise Pascal Jian-Guo Liu University of Maryland Yue-Jun Peng Université Blaise Pascal

Numerical Analysis and Scientific Computing mathscidoc:1702.25048

Mathematical Modelling and Numerical Analysis, 37, (2), 319–338., 2003.3
We introduce a finite volume scheme for multi-dimensional drift-diffusion equations. Such equations arise from the theory of semiconductors and are composed of two continuity equations coupled with a Poisson equation. In the case that the continuity equations are non degenerate, we prove the convergence of the scheme and then the existence of solutions to the problem. The key point of the proof relies on the construction of an approximate gradient of the electric potential which allows us to deal with coupled terms in the continuity equations. Finally, a numerical example is given to show the efficiency of the scheme.
Finite volume scheme, drift-diffusion equations, approximation of gradient
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@inproceedings{claire2003finite,
  title={Finite volume scheme for multi-dimensional drift-diffusion equations and convergence analysis},
  author={Claire Chainais-Hillairet, Jian-Guo Liu, and Yue-Jun Peng},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170209103706791929378},
  booktitle={Mathematical Modelling and Numerical Analysis},
  volume={37},
  number={2},
  pages={319–338.},
  year={2003},
}
Claire Chainais-Hillairet, Jian-Guo Liu, and Yue-Jun Peng. Finite volume scheme for multi-dimensional drift-diffusion equations and convergence analysis. 2003. Vol. 37. In Mathematical Modelling and Numerical Analysis. pp.319–338.. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170209103706791929378.
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