Finite volume element approximation and analysis for a kind of semiconductor device simulation (Q980422)

This paper deals with a class of two-dimensional semiconductor problems, which are solved by using the finite volume element method. There are also established the convergence rates of the discretization schemes under general conditions. A fully discrete finite volume element scheme with different time steps is given for the semiconductor problem. The authors prove an optimal error estimate of order \(O(h+\Delta t+(\Delta\bar t^0)^{3/2}+(\Delta\bar t)^2)\) in \(H^1\)-norm.