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Displaying similar documents to “On the analysis of Bérenger's Perfectly Matched Layers for Maxwell's equations”

A linear mixed finite element scheme for a nematic Ericksen–Leslie liquid crystal model

F. M. Guillén-González, J. V. Gutiérrez-Santacreu (2013)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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In this work we study a fully discrete mixed scheme, based on continuous finite elements in space and a linear semi-implicit first-order integration in time, approximating an nematic liquid crystal model by means of a penalized problem. Conditional stability of this scheme is proved a discrete version of the energy law satisfied by the continuous problem, and conditional convergence towards generalized Young measure-valued solutions to the problem is showed when the discrete parameters...

Asymptotic stability of stationary solutions to the drift-diffusion model in the whole space

Ryo Kobayashi, Masakazu Yamamoto, Shuichi Kawashima (2012)

ESAIM: Control, Optimisation and Calculus of Variations

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We study the initial value problem for the drift-diffusion model arising in semiconductor device simulation and plasma physics. We show that the corresponding stationary problem in the whole space ℝ admits a unique stationary solution in a general situation. Moreover, it is proved that when  ≥ 3, a unique solution to the initial value problem exists globally in time and converges to the corresponding stationary solution as time tends to infinity, provided that the amplitude of the stationary...