Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4642233 | Journal of Computational and Applied Mathematics | 2009 | 11 Pages |
Abstract
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.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
René Pinnau, Jorge Mauricio Ruiz V,