A Positivity-preserving Numerical Scheme for a Nonlinear Fourth Order Parabolic System

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2000
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Jüngel, Ansgar
Pinnau, René
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A positivity-preserving numerical scheme for a fourth order nonlinear parabolic system arising in quantum semiconductor modelling is studied. The system is numerically treated by introducing an additional nonlinear potential and a subsequent semidiscretization in time. The resulting sequence of nonlinear second order elliptic systems admits at each time level strictly positive solutions, which is proved by an exponential transformation of variables. The stability of the scheme is shown and convergence is proved in one space dimension. The results extend under additional assumptions to the multi-dimensional case. Assuming enough regularity on the solution the rate of convergence proves to be optimal. Numerical results concerning the switching behaviour of a resonant tunneling diode are presented.

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ISO 690JÜNGEL, Ansgar, René PINNAU, 2000. A Positivity-preserving Numerical Scheme for a Nonlinear Fourth Order Parabolic System
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@unpublished{Jungel2000Posit-6224,
  year={2000},
  title={A Positivity-preserving Numerical Scheme for a Nonlinear Fourth Order Parabolic System},
  author={Jüngel, Ansgar and Pinnau, René}
}
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