Error Estimates for a Finite Element Method for the Drift-diffusion Semiconductor Device Equations: the Zero Diffusion Case
نویسنده
چکیده
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'J-error between the approximate and exact electron concentrations of the zero-diffusion unipolar model is of order Ax1/2 . These estimates are sharp.
منابع مشابه
Error Estimates for a Finite Element Method for the Drift-diffusion Semiconductor Device Equations
In this paper, optimal error estimates are obtained for a method for numerically solving the so-called unipolar model (a one-dimensional simpliied version of the drift-diiusion semiconductor device equations). The numerical method combines a mixed nite element method using a continuous piecewise-linear approximation of the electric eld with an explicit upwinding nite element method using a piec...
متن کاملA posteriori $ L^2(L^2)$-error estimates with the new version of streamline diffusion method for the wave equation
In this article, we study the new streamline diffusion finite element for treating the linear second order hyperbolic initial-boundary value problem. We prove a posteriori $ L^2(L^2)$ and error estimates for this method under minimal regularity hypothesis. Test problem of an application of the wave equation in the laser is presented to verify the efficiency and accuracy of the method.
متن کاملNumerical method for singularly perturbed fourth order ordinary differential equations of convection-diffusion type
In this paper, we have proposed a numerical method for singularly perturbed fourth order ordinary differential equations of convection-diffusion type. The numerical method combines boundary value technique, asymptotic expansion approximation, shooting method and finite difference method. In order to get a numerical solution for the derivative of the solution, the given interval is divided in...
متن کاملA new exponentially fitted triangular finite element method for the continuity equations in the drift-diffusion model of semiconductor devices
In this paper we present a novel exponentially fitted finite element method with triangular éléments for the decoupled continuity équations in the drift-diffusion model of semiconductor devices. The continuous problem is first formulated as a variational problem using a weighted inner product. A Bubnov-Galerkin finite element method with a set of piecewise exponential basis functions is then pr...
متن کاملA Finite Element Method for Time-dependent Convection-diffusion Equations
We present a finite element method for time-dependent convectiondiffusion equations. The method is explicit and is applicable with piecewise polynomials of degree n > 2 . In the limit of zero diffusion, it reduces to a recently analyzed finite element method for hyperbolic equations. Near optimal error estimates are derived. Numerical results are given.
متن کامل