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

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- by Bernardo Cockburn and Ioana Triandaf PDF
- Math. Comp.
**63**(1994), 51-76 Request permission

## 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

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## Additional Information

- © Copyright 1994 American Mathematical Society
- Journal: Math. Comp.
**63**(1994), 51-76 - MSC: Primary 65M60; Secondary 35L60
- DOI: https://doi.org/10.1090/S0025-5718-1994-1226812-8
- MathSciNet review: 1226812