Difference streamline diffusion method for three-dimensional semiconductor problem with heat-condution (Q2735402)

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.