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On some recent results on the numerical problems in semiconductor device simulation. (English) Zbl 0713.65082
Differential equations and their applications, Proc. 7th Conf., Equadiff 7, Prague/Czech. 1989, Teubner-Texte Math. 118, 9-17 (1990).
[For the entire collection see Zbl 0704.00019.]
The following problem is discussed: find \(\rho \in H^ 1(\Omega)\) such that \(-div(e^{-\psi}\nabla \rho)=f\) in \(\Omega,\rho =\chi:=e^{\psi}g\) on \(\Gamma_ 0\), \(\frac{\partial \rho}{\partial n}=0\) on \(\Gamma_ 1\), \(\Gamma_ 0\cup \Gamma_ 1=\partial \Omega\), where \(\psi\) is assumed to be known, f,g are functions independent of \(\rho\). The asymptotic behaviour of the numerical solution is investigated when the electric field \(E=-\nabla \psi\) is very large in some parts of the domain \(\Omega\).
Reviewer: L.G.Vulkov
65Z05 Applications to the sciences
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
35Q60 PDEs in connection with optics and electromagnetic theory
78M10 Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory
78A55 Technical applications of optics and electromagnetic theory
Zbl 0704.00019