Rational design of field-effect sensors using partial differential equations, Bayesian inversion, and artificial neural networks
Silicon nanowire field-effect transistors are promising devices used to detect minute
amounts of different biological species. We introduce the theoretical and computational …
amounts of different biological species. We introduce the theoretical and computational …
An adaptive multilevel Monte Carlo algorithm for the stochastic drift–diffusion–Poisson system
We present an adaptive multilevel Monte Carlo algorithm for solving the stochastic drift–
diffusion–Poisson system with non-zero recombination rate. The a-posteriori error is …
diffusion–Poisson system with non-zero recombination rate. The a-posteriori error is …
Asymptotic behaviour of a finite-volume scheme for the transient drift-diffusion model
C Chainais-Hillairet, F Filbet - IMA journal of numerical analysis, 2007 - academic.oup.com
In this paper, we propose a finite-volume discretization for multidimensional nonlinear drift-
diffusion system. Such a system arises in semiconductors modelling and is composed of two …
diffusion system. Such a system arises in semiconductors modelling and is composed of two …
Finite volume approximation for degenerate drift-diffusion system in several space dimensions
C Chainais-Hillairet, YJ Peng - Mathematical Models and Methods …, 2004 - World Scientific
This paper is devoted to a finite volume discretization for multidimensional nonlinear drift-
diffusion system. Such system arises in semiconductors modelling and is composed of two …
diffusion system. Such system arises in semiconductors modelling and is composed of two …
Asymptotic-preserving and well-balanced schemes for the 1D Cattaneo model of chemotaxis movement in both hyperbolic and diffusive regimes
L Gosse - Journal of Mathematical Analysis and Applications, 2012 - Elsevier
The original Well-Balanced (WB) framework of Greenberg and LeRoux (1996)[24] and
Gosse (2002)[18] relying on Non-Conservative (NC) products (see LeFoch and Tzavaras …
Gosse (2002)[18] relying on Non-Conservative (NC) products (see LeFoch and Tzavaras …
Analysis of a finite element method for the drift-diffusion semiconductor device equations: the multidimensional case
Z Chen, B Cockburn - Numerische Mathematik, 1995 - Springer
An explicit finite element method for numerically solving the drift-diffusion semiconductor
device equations in two space dimensions is analyzed. The method is based on the use of a …
device equations in two space dimensions is analyzed. The method is based on the use of a …
Error estimates for a finite element method for the drift diffusion semiconductor device equations
Z Chen, B Cockburn - SIAM journal on numerical analysis, 1994 - SIAM
In this paper, optimal error estimates are obtained for a method for numerically solving the
so-called unipolar model (a one-dimensional simplified version of the drift-diffusion semi …
so-called unipolar model (a one-dimensional simplified version of the drift-diffusion semi …
Stability and convergence of a finite element method for reactive transport in ground water
Z Chen, RE Ewing - SIAM journal on numerical analysis, 1997 - SIAM
An explicit finite element method is used to solve the linear convection--diffusion-reaction
equations governing contaminant transport in ground water flowing through an adsorbing …
equations governing contaminant transport in ground water flowing through an adsorbing …
Numerical analysis of a mean field model of superconducting vortices
CM Elliott, V Styles - IMA journal of numerical analysis, 2001 - ieeexplore.ieee.org
A finite volume/element approximation of a mean field model of superconducting vortices in
one and two dimensions is presented. The solutions of these approximations are …
one and two dimensions is presented. The solutions of these approximations are …
Blow-up of solutions for a class of balance laws
R Natalini, A Tesei - Communications in partial differential …, 1994 - Taylor & Francis
Blow-up of solutions for a class of balance laws Page 1 COMMUN. IN PARTIAL DIFFERENTIAL
EQUATIONS, 19(3&4), 417-453 (1994) BLOW-UP OF SOLUTIONS FOR A CLASS OF …
EQUATIONS, 19(3&4), 417-453 (1994) BLOW-UP OF SOLUTIONS FOR A CLASS OF …