Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



Error estimates for a finite element method for the drift-diffusion semiconductor device equations: the zero diffusion case

Authors: Bernardo Cockburn and Ioana Triandaf
Journal: Math. Comp. 63 (1994), 51-76
MSC: Primary 65M60; Secondary 35L60
MathSciNet review: 1226812
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper new error estimates for an explicit finite element method for numerically solving the so-called zero-diffusion unipolar model (a one-dimensional simplified version of the drift-diffusion semiconductor device equations) are obtained. The method, studied in a previous paper, combines a mixed finite element method using a continuous piecewise-linear approximation of the electric field, with an explicit upwinding finite element method using a piecewise-constant approximation of the electron concentration. By using a suitable extension of Kuznetsov approximation theory for scalar conservation laws, it is proved that, under proper hypotheses on the data, the ${L^\infty }({L^1})$-error between the approximate and exact electron concentrations of the zero-diffusion unipolar model is of order $\Delta {x^{1/2}}$. These estimates are sharp.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65M60, 35L60

Retrieve articles in all journals with MSC: 65M60, 35L60

Additional Information

Keywords: Semiconductor devices, conservation laws, finite elements, convergence
Article copyright: © Copyright 1994 American Mathematical Society