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S. Gadau, A. Jüngel:
"A three-dimensional mixed finite-element approximation of the semiconductor energy-transport equations";
SIAM Journal on Scientific Computing, 31 (2008), 1120 - 1140.

The stationary energy-transport equations for semiconductors in three space dimensions
are numerically discretized. The physical variables are the electron density, the energy density,
and the electric potential. Physically motivated mixed Dirichlet-Neumann boundary conditions are
employed. The numerical approximation is based on a hybridized mixed finite-element method with
Raviart-Thomas-N´ed´elec elements, applied to the dual-entropy formulation of the energy-transport
model. For the solution of the nonlinear discrete system, a Newton scheme with adaptive potential
stepping and two decoupling Gummel-type strategies with reduced rank extrapolation are proposed.
Multigate field-effect transistors in two dimensions and three dimensions are numerically simulated.

Siehe englisches Abstract.

energy-transport equations, dual-entropy variables, cross-diffusion system