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A mass-lumping semidiscretization of the semiconductor device equations. I: Properties of the semidiscrete problem. (English) Zbl 0687.65113
The system of partial differential equations \(-q\Delta u_ 0=u_ 2-u_ 1+Q,\quad (u_ 1)_ t=\nabla \cdot J_ 1-S(u_ 1,u_ 2),\quad (u_ 2)_ t=-\nabla \cdot J_ 2-S(u_ 1,u_ 2),\quad J_ 1=\nabla u_ 1- u_ 1\nabla u_ 0,\quad J_ 2=-p(\nabla u_ 2+u_ 2\nabla u_ 0)\) is investigated in a cylinder with a method which can be regarded as a combination of finite difference and finite element ideas.
Reviewer: L.A.Sakhnovich

MSC:
65Z05 Applications to the sciences
65N22 Numerical solution of discretized equations for boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
78A55 Technical applications of optics and electromagnetic theory
35Q99 Partial differential equations of mathematical physics and other areas of application
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References:
[1] Adams R.A., New York-San Francisco-London (1975)
[2] Gajewski H., On the basic equations for carrier transport in semiconductors. Preprint P-MATH-39/84. AdW der DDR (1984) · Zbl 0562.35022
[3] Brezzi F., Instituto di Analisi Numerica (1985)
[4] Ciarlet P., The Finite Element Method for Elliptic Problems (1978) · Zbl 0383.65058
[5] Cottrell P.E., Proc. NASECODE I Conf., 31-64 (1979)
[6] Engl W.L., Proc. NASECODE I Conf., 65-93 (1979)
[7] Grisvard P., Elliptic Problems in Nonsmooth Domains (1985) · Zbl 0695.35060
[8] DOI: 10.1002/mana.19871320119 · Zbl 0639.35008 · doi:10.1002/mana.19871320119
[9] DOI: 10.1109/T-ED.1964.15364 · doi:10.1109/T-ED.1964.15364
[10] DOI: 10.1007/978-3-0348-7196-9 · doi:10.1007/978-3-0348-7196-9
[11] Henry D., Lecture Notes in Mathematics 841, in: Geometric theory of semilinear parabolic equations (1981) · Zbl 0456.35001 · doi:10.1007/BFb0089647
[12] Ikeda T., Maximum Principle in Finite Element Models for Convection-diffusion Phenomena (1983) · Zbl 0508.65049
[13] Mazja V.G., Zeitschrift für Analysis und ihre Anwendungen 2 (1983) 335-359 pp 523–
[14] P.A. Markowich, C.A. Ringhofer, E. Langer and S. Selberherr, An asymptotic analysis of single-junction semiconductor devices. MRC Technical Summary Report 2527, Mathematics Research Center, Universityof Wisconsin, Madison,1983.
[15] DOI: 10.1108/eb009978 · Zbl 0619.65115 · doi:10.1108/eb009978
[16] McCartin B.J., Lecture notes of a short course held in association with the NASECODE IV conf. (ed.: J.J.H. Miller) pp 72– (1985)
[17] Miller J.J.H., Numerical Analysis of Semiconductor Devices and Integrated Circuits (1983)
[18] DOI: 10.1090/S0025-5718-1982-0645661-4 · doi:10.1090/S0025-5718-1982-0645661-4
[19] Roos H.-G., Dresden (1986)
[20] DOI: 10.1109/T-ED.1969.16566 · doi:10.1109/T-ED.1969.16566
[21] DOI: 10.1109/T-ED.1973.17727 · doi:10.1109/T-ED.1973.17727
[22] Thomeé V., Lecture Notes in Mathematics 1054, in: Galerkin finite element methods for parabolic problems (1984)
[23] Vasil’eva A.B., J. on Comput. Mathematics and Mathem. Physics 17 pp 339– (1977)
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