Math @ Duke

Publications [#246952] of JianGuo Liu
Papers Published
 ChainaisHillairet, C; Liu, JG; Peng, YJ, Finite volume scheme for multidimensional driftdiffusion equations and convergence analysis,
Mathematical Modelling and Numerical Analysis, vol. 37 no. 2
(2003),
pp. 319338
(last updated on 2018/10/14)
Abstract: We introduce a finite volume scheme for multidimensional driftdiffusion 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.


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