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A mass-lumping semidiscretization of the semiconductor device equations. I: Properties of the semidiscrete problem. (English) Zbl 0687.65113
The system of partial differential equations $$-q\Delta u_ 0=u_ 2-u_ 1+Q,\quad (u_ 1)_ t=\nabla \cdot J_ 1-S(u_ 1,u_ 2),\quad (u_ 2)_ t=-\nabla \cdot J_ 2-S(u_ 1,u_ 2),\quad J_ 1=\nabla u_ 1- u_ 1\nabla u_ 0,\quad J_ 2=-p(\nabla u_ 2+u_ 2\nabla u_ 0)$$ is investigated in a cylinder with a method which can be regarded as a combination of finite difference and finite element ideas.
Reviewer: L.A.Sakhnovich

MSC:
 65Z05 Applications to the sciences 65N22 Numerical solution of discretized equations for boundary value problems involving PDEs 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 78A55 Technical applications of optics and electromagnetic theory 35Q99 Partial differential equations of mathematical physics and other areas of application
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