For three-dimensional transient behavior of semiconductor problems   of heat conduction, a semi-discretization and a full-discretization  based on block-centered finite differences and nonuniform partitions are presented in this paper. In consideration of mixed finite element method, duality principle, induction hypothesis, prior error theory and special techniques of partial differential equations, second-order error estimates in discrete  norm are derived. Specially, the superconvergence scheme, approximating electric field intensity, has an important position in actual applications.

transient behavior of a semiconductor device of heat conduction, semi-discretization and full-discretization based on block-centered finite differences and nonuniform partitions, mixed element method, second order error estimates in discrete  norm, superconvergence of electric field intensity computation.