Brezzi, Franco; Marini, Luisa Donatella; Pietra, Paola Two-dimensional exponential fitting and applications to drift-diffusion models. (English) Zbl 0686.65088 SIAM J. Numer. Anal. 26, No. 6, 1342-1355 (1989). The authors consider the numerical solution for u of the two-dimensional system \(\nabla \cdot (\nabla u+u\nabla \psi)=f\quad in\quad \Omega,\quad u=g\) on \(\Gamma_ 0\subset \partial \Omega;\quad \partial u/\partial n+u(\partial \psi /\partial n)=0\) on \(\Gamma_ 1=\partial \Omega \setminus \Gamma_ 0,\) when \(\psi\), f and g are given. \(\nabla \psi\) can be large and so the transformation \(u=\rho \exp (-\psi)\) is used. They develop a number of methods for the discretization of the system, all of which involve the conservation of \(J=\nabla u+u\nabla \psi,\) and show that unique solutions exist. The results of the application of the ideas discussed to a particular problem are given. Reviewer: Ll.G.Chambers Cited in 5 ReviewsCited in 71 Documents MSC: 65Z05 Applications to the sciences 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 35Q99 Partial differential equations of mathematical physics and other areas of application 78A55 Technical applications of optics and electromagnetic theory Keywords:drift-diffusion models; exponential fitting; upwind; mixed finite element method; semiconductors PDF BibTeX XML Cite \textit{F. Brezzi} et al., SIAM J. Numer. Anal. 26, No. 6, 1342--1355 (1989; Zbl 0686.65088) Full Text: DOI OpenURL