Zhang, Zhengru Difference streamline diffusion method for three-dimensional semiconductor problem with heat-condution. (Chinese. English summary) Zbl 0991.65098 J. Shandong Univ., Nat. Sci. Ed. 36, No. 1, 22-30 (2001). The author studies the numerical approximation for a three-dimensional semiconductor model with heat-diffusion. The model consists of a coupled system of elliptic, convection-diffusion and heat-diffusion equations. Considering the feature of the equations in the system, the author presents a discrete scheme by applying the mixed finite element method for the elliptic equation, the difference streamline-diffusion method for the convection-diffusion equations and the standard finite element method for the heat-diffusion equation. By exploiting the properties of the finite element interpolation spaces and the elliptic projection, and using discrete energy estimates, the author proves the existence and uniqueness of approximate solutions and obtains the quasi-optimal \(L^2\)-error estimate provided that the exact solutions are sufficiently regular. Reviewer: Song Jiang (Beijing) MSC: 65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs 65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs 65M25 Numerical aspects of the method of characteristics for initial value and initial-boundary value problems involving PDEs 65M15 Error bounds for initial value and initial-boundary value problems involving PDEs 82D37 Statistical mechanics of semiconductors 35Q72 Other PDE from mechanics (MSC2000) 35M10 PDEs of mixed type Keywords:3D semiconductor with heat-diffusion; difference streamline-diffusion method; characteristic difference scheme; quasi-optimal error estimate; mixed finite element method; convection-diffusion equations; heat-diffusion equation PDFBibTeX XMLCite \textit{Z. Zhang}, J. Shandong Univ., Nat. Sci. Ed. 36, No. 1, 22--30 (2001; Zbl 0991.65098)