zbMATH — the first resource for mathematics

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

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
Full Text: DOI