Finite element solution of the fundamental equations of semiconductor devices. II

Miloš Zlámal

Applications of Mathematics (2001)

  • Volume: 46, Issue: 4, page 251-294
  • ISSN: 0862-7940

Abstract

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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].

How to cite

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Zlámal, Miloš. "Finite element solution of the fundamental equations of semiconductor devices. II." Applications of Mathematics 46.4 (2001): 251-294. <http://eudml.org/doc/33087>.

@article{Zlámal2001,
abstract = {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].},
author = {Zlámal, Miloš},
journal = {Applications of Mathematics},
keywords = {semiconductor devices; finite element method; fully discrete approximate solution; convergence; minimum angle condition; unconditionally stable schemes; fully discrete solutions; finite element method; evolution nonlinear system; semiconductor equations; convergence; finite difference scheme},
language = {eng},
number = {4},
pages = {251-294},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Finite element solution of the fundamental equations of semiconductor devices. II},
url = {http://eudml.org/doc/33087},
volume = {46},
year = {2001},
}

TY - JOUR
AU - Zlámal, Miloš
TI - Finite element solution of the fundamental equations of semiconductor devices. II
JO - Applications of Mathematics
PY - 2001
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 46
IS - 4
SP - 251
EP - 294
AB - 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].
LA - eng
KW - semiconductor devices; finite element method; fully discrete approximate solution; convergence; minimum angle condition; unconditionally stable schemes; fully discrete solutions; finite element method; evolution nonlinear system; semiconductor equations; convergence; finite difference scheme
UR - http://eudml.org/doc/33087
ER -

References

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  13. 10.1090/S0025-5718-1986-0815829-6, Math. Comp. 46 (1986), 27–43. (1986) MR0815829DOI10.1090/S0025-5718-1986-0815829-6
  14. Finite element solution of the fundamental equations of semiconductor devices, In: Numerical Approximation of Partial Differential Equations (E. L. Ortiz, ed.), North-Holland, Amsterdam-New York-Oxford-Tokyo, 1987, pp. 121–128. (1987) MR0899784
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