Chen, Z. Hybrid variable finite elements for semiconductor devices. (English) Zbl 0705.65097 Comput. Math. Appl. 19, No. 4, 65-73 (1990). 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 Cited in 2 Documents 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 Keywords:hybrid variable finite elements; semiconductor devices; Galerkin method; error estimate Citations:Zbl 0686.65088 PDFBibTeX XMLCite \textit{Z. Chen}, Comput. Math. Appl. 19, No. 4, 65--73 (1990; Zbl 0705.65097) 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 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.