## 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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