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Two-dimensional exponential fitting and applications to drift-diffusion models. (English) Zbl 0686.65088
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

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
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