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higher order parabolic pde

ESAIM: Mathematical Modelling and Numerical Analysis (1)

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Convergent semidiscretization of a nonlinear fourth order parabolic system
Ansgar Jüngel, René Pinnau
Journal:

ESAIM: Mathematical Modelling and Numerical Analysis / Volume 37 / Issue 2 / March 2003

Published online by Cambridge University Press:

15 November 2003, pp. 277-289

Print publication:

March 2003
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A semidiscretization in time of a fourth order nonlinear parabolic system in several space dimensions arising in quantum semiconductor modelling is studied. The system is numerically treated by introducing an additional nonlinear potential. Exploiting the stability of the discretization, convergence is shown in the multi-dimensional case. Under some assumptions on the regularity of the solution, the rate of convergence proves to be optimal.