Finite difference method and analysis for three-dimensional semiconductor device of heat conduction (Q674709)

The mathematical model of the three-dimensional semiconductor devices of heat conduction is described by a system of four quasilinear partial differential equations for initial-boundary value problems. One equation in elliptic form is for the electric potential; two equations of convection-dominated diffusion type are for the electron and hole concentration; and one heat conduction equation is for temperature. Characteristic finite difference schemes for two kinds of boundary value problems are put forward. By using thick and thin grids to form a complete set and treating the product threefold-quadratic interpolation, a variable time step method with the boundary condition, calculus of variations and the theory of prior estimates and techniques, optimal error estimates in \(L^2\) norm are derived in the approximate solutions.