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**Hybrid variable finite elements for semiconductor devices.**
*(English)*
Zbl 0705.65097

The paper is devoted to the numerical solution of partial differential equations in two dimensions. The technique of hybrid variable finite elements for semiconductor devices is employed. Main result: The author shows that the system arising from the method proposed by F. Brezzi, L. D. Marini and P. Pietra for the solution of semiconductor device equations [SIAM J. Numer. Anal. 26, No.6, 1342-1355 (1989; Zbl 0686.65088)] has essentially diagonal matrices, and that, by use of a certain numerical integration, the methods are identical with the classical Galerkin method. Moreover the paper indicates how the methods generalize to a more general case (in which the function \(\psi\) might depend on u). Very important aspect of this work is the error estimate for the approximation of current, \((=\sigma =\nabla u+u\nabla \psi)\).

Reviewer: J.Lovíšek

### MSC:

65Z05 | Applications to the sciences |

65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |

65N15 | Error bounds for boundary value problems involving PDEs |

35Q60 | PDEs in connection with optics and electromagnetic theory |

78A55 | Technical applications of optics and electromagnetic theory |

### Citations:

Zbl 0686.65088
Full Text:
DOI

### References:

[1] | F. Brezzi, L.D. Marini and P. Pietra, Two-dimensional exponential fitting and application to semiconductor device equations. SIAM Jl numer. Analysis; F. Brezzi, L.D. Marini and P. Pietra, Two-dimensional exponential fitting and application to semiconductor device equations. SIAM Jl numer. Analysis · Zbl 0686.65088 |

[2] | Brezzi, F., On the existence, uniqueness and approximation of saddlepoint problems arising from Lagrangian multipliers, RAIRO, 8-R2, 129-151 (1974) · Zbl 0338.90047 |

[3] | Babuško, I.; Osborn, J., Generalized finite element methods: their perfomance and their relation to mixed methods, SIAM Jl numer. Analysis, 20, 510-536 (1983) · Zbl 0528.65046 |

[4] | Engels, H., Numerical Quadrature and Cubature (1980), Academic Press: Academic Press New York · Zbl 0435.65013 |

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