Article
MSC:
35Q60,
65M06,
65M12,
65M60,
65N12,
65N30,
82D37 | MR 1842551 | Zbl 1066.65107 | DOI: 10.1023/A:1013748108936
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Keywords:
semiconductor devices; finite element method; fully discrete approximate solution; convergence
semiconductor devices; finite element method; fully discrete approximate solution; convergence
Summary:
In part I of the paper (see Zlámal [13]) finite element solutions of the nonstationary semiconductor equations were constructed. Two fully discrete schemes were proposed. One was nonlinear, the other partly linear. In this part of the paper we justify the nonlinear scheme. We consider the case of basic boundary conditions and of constant mobilities and prove that the scheme is unconditionally stable. Further, we show that the approximate solution, extended to the whole time interval as a piecewise linear function, converges in a strong norm to the weak solution of the semiconductor equations. These results represent an extended and corrected version of results announced without proof in Zlámal [14].
References:
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