Study of a Finite Volume Scheme for the Drift-Diffusion System. Asymptotic Behavior in the Quasi-Neutral Limit

Bessemoulin-Chatard, Marianne; Chainais-Hillairet, Claire; Vignal, Marie-Hélène

doi:10.1137/130913432

Cited by 33 publications

(32 citation statements)

References 46 publications

(126 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In this section, we prove Theorem . The proof of existence is done by induction on n and we follow some ideas developed in . Let us note that the element s 0 is defined by (14) and the vectors u 0 and v 0 are defined by (15).…”

Section: Existence Of a Solution To The Schemementioning

confidence: 99%

See 1 more Smart Citation

Numerical approximation of a concrete carbonation model: Study of the ‐law of propagation

Zurek

2019

Numerical Methods Partial

View full text Add to dashboard Cite

In this paper, we are interested in the long time behavior of approximate solutions to a free boundary model which appears in the modeling of concrete carbonation [1]. In particular, we study the long time regime of the moving interface. The numerical solutions are obtained by an implicit in time and finite volume in space scheme. We show the existence of solutions to the scheme and, following [2‐3], we prove that the approximate free boundary increases in time following a t‐law. Finally, we supplement the study through numerical experiments.

show abstract

Section: Existence Of a Solution To The Schemementioning

confidence: 99%

“…The proof of existence is done by induction on n and we follow some ideas developed in [14]. Let us note that the element s 0 is defined by (14) and the vectors u 0 and v 0 are defined by (15). Hypothesis (A7) ensures that u 0 and v 0 fulfill the condition (19).…”

Section: Existence Of a Solution To The Schemementioning

confidence: 99%

Numerical approximation of a concrete carbonation model: Study of the ‐law of propagation

Zurek

2019

Numerical Methods Partial

View full text Add to dashboard Cite

show abstract

“…The parameter μ > 0 allows us to prove unconditional stability for the linearized problem; see for example [22]. The corresponding term vanishes for fixed points ρ T = n T , so that a fixed point for F k μ is a solution to scheme (20)-(27).…”

Section: A Existence Of a Solution To The Schemementioning

confidence: 99%

“…Let (n k ±,T , V k T ) k≥0 be a solution to (22), (55) with the corresponding Dirichlet-Neumann boundary conditions. As we have to deal with the logarithm of the densities n k ±,K , which may vanish, we introduce a regularization of the discrete free energy.…”

Section: Proof Of Theoremmentioning

confidence: 99%

See 1 more Smart Citation

A finite-volume scheme for a spinorial matrix drift-diffusion model for semiconductors

Chainais-Hillairet

Jüngel

Shpartko

2015

Numer. Methods Partial Differential Eq.

View full text Add to dashboard Cite

International audienceAn implicit Euler finite-volume scheme for a spinorial matrix drift-diffusion model for semiconductors is analyzed. The model consists of strongly coupled parabolic equations for the electron density matrix or, alternatively, of weakly coupled equations for the charge and spin-vector densities, coupled to the Poisson equation for the elec-tric potential. The equations are solved in a bounded domain with mixed Dirichlet-Neumann boundary conditions. The charge and spin-vector fluxes are approximated by a Scharfetter-Gummel discretization. The main features of the numerical scheme are the preservation of positivity and L ∞ bounds and the dissipation of the discrete free energy. The existence of a bounded discrete solution and the monotonicity of the discrete free energy are proved. For undoped semiconductor materials, the numerical scheme is uncon-ditionally stable. The fundamental ideas are reformulations using spin-up and spin-down densities and certain projections of the spin-vector density, free energy estimates, and a discrete Moser iteration. Furthermore, numerical simulations of a simple ferromagnetic-layer field-effect transistor in two space dimensions are presented

show abstract

Finite Volume Methods: Foundation and Analysis

Barth

Herbin

Ohlberger

2017

Encyclopedia of Computational Mechanics Second Edition

View full text Add to dashboard Cite

Finite volume methods are a class of discretization schemes that have proven highly successful in approximating the solution of a wide variety of conservation law systems. They are extensively used in fluid mechanics, porous media flow, meteorology, electromagnetics, models of biological processes, semi-conductor device simulation and many other engineering areas governed by conservative systems that can be written in integral control volume form.This article reviews elements of the foundation and analysis of modern finite volume methods.The primary advantages of these methods are numerical robustness through the obtention of discrete maximum (minimum) principles, applicability on very general unstructured meshes, and the intrinsic local conservation properties of the resulting schemes. Throughout this article, specific attention is given to scalar nonlinear hyperbolic conservation laws and the development of high order accurate schemes for discretizing them. A key tool in the design and analysis of finite volume schemes suitable for non-oscillatory discontinuity capturing is discrete maximum principle analysis. A number of building blocks used in the development of numerical schemes possessing local discrete maximum principles are reviewed in one and several space dimensions, e.g. monotone fluxes, E-fluxes, TVD discretization, nonoscillatory reconstruction, slope limiters, positive coefficient schemes, etc. When available, theoretical results concerning a priori and a posteriori error estimates are given. Further advanced topics are then considered such as high order time integration, discretization of dffision terms and the extension to systems of nonlinear conservation laws.

show abstract

Study of a Finite Volume Scheme for the Drift-Diffusion System. Asymptotic Behavior in the Quasi-Neutral Limit

Cited by 33 publications

References 46 publications

Numerical approximation of a concrete carbonation model: Study of the ‐law of propagation

Numerical approximation of a concrete carbonation model: Study of the ‐law of propagation

A finite-volume scheme for a spinorial matrix drift-diffusion model for semiconductors

Finite Volume Methods: Foundation and Analysis

Contact Info

Product

Resources

About