The stationary semiconductor device equations
The stationary semiconductor device equations
Nonlinear functional analysis and its applications
Nonlinear functional analysis and its applications
Semiconductor equations
On the stationary quantum drift-diffusion model
Zeitschrift für Angewandte Mathematik und Physik (ZAMP)
The Stationary Current-Voltage Characteristics of the Quantum Drift-Diffusion Model
SIAM Journal on Numerical Analysis
Finite Element Method for Elliptic Problems
Finite Element Method for Elliptic Problems
A Positivity-Preserving Numerical Scheme for a Nonlinear Fourth Order Parabolic System
SIAM Journal on Numerical Analysis
Uniform Convergence of an Exponentially Fitted Scheme for the Quantum Drift Diffusion Model
SIAM Journal on Numerical Analysis
Quantum-corrected drift-diffusion models for transport in semiconductor devices
Journal of Computational Physics
| Hi-index | 7.29 |
We study nonlinear finite element discretizations for the density gradient equation in the quantum drift diffusion model. In particular, we give a finite element description of the so-called nonlinear scheme introduced by Ancona. We prove the existence of discrete solutions and provide a consistency and convergence analysis, which yields the optimal order of convergence for both discretizations. The performance of both schemes is compared numerically, in particular, with respect to the influence of approximate vacuum boundary conditions.