ISSN:
0749-159X
Keywords:
Mathematics and Statistics
;
Numerical Methods
Source:
Wiley InterScience Backfile Collection 1832-2000
Topics:
Mathematics
Notes:
In this article we deal with the solution in Ω ⊂ R2 of the quasi linear equation -Δu = f(x, y, u(x, y)) subject to mixed boundary data and representing Gauss' law in a semiconductor device, where u and f are, respectively, the electrostatic potential and the space charge density after a suitable scaling. In the following we consider the associated variational problem of finding in a suitable subspace of H1(Ω) the minimum of the functional \documentclass{article}\pagestyle{empty}\begin{document}$ J(u)\, = \,\int {_\Omega } (\frac{1}{2}\left| {\nabla u\left| {^2 \, - \,{\cal F}(x,y,u)\,d\Omega,} \right.} \right. $\end{document}, where \documentclass{article}\pagestyle{empty}\begin{document}$ {\cal F}(x,y,u)\, = \,\int f (x,y,\xi)\,d\xi, $\end{document} and we prove existence and uniqueness of a weak solution according to the technique of Convex Analysis. The numerical study is then carried on by a piecewise linear finite element approximation, which is proved to converge in the H1-norm to the exact solution of the variational problem; some numerical examples are also included. © 1994 John Wiley & Sons, Inc.
Additional Material:
17 Ill.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1002/num.1690100607
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