Hybrid variable finite elements for semiconductor devices (Q918175)

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 \textit{F. Brezzi}, \textit{L. D. Marini} and \textit{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, \((=\sigma =\nabla u+u\nabla \psi)\).