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Numerical analysis of the planewave discretization of some orbital-free and Kohn-Sham models

Eric Cancès, Rachida Chakir, Yvon Maday (2011)

ESAIM: Mathematical Modelling and Numerical Analysis

In this article, we provide a priori error estimates for the spectral and pseudospectral Fourier (also called planewave) discretizations of the periodic Thomas-Fermi-von Weizsäcker (TFW) model and for the spectral discretization of the periodic Kohn-Sham model, within the local density approximation (LDA). These models allow to compute approximations of the electronic ground state energy and density of molecular systems in the condensed phase. The TFW model is strictly convex with respect to the...

Numerical analysis of the quasistatic thermoviscoelastic thermistor problem

José R. Fernández (2006)

ESAIM: Mathematical Modelling and Numerical Analysis

In this work, the quasistatic thermoviscoelastic thermistor problem is considered. The thermistor model describes the combination of the effects due to the heat, electrical current conduction and Joule's heat generation. The variational formulation leads to a coupled system of nonlinear variational equations for which the existence of a weak solution is recalled. Then, a fully discrete algorithm is introduced based on the finite element method to approximate the spatial variable and an Euler scheme...

Numerical homogenization for indefinite H(curl)-problems

Verfürth, Barbara (2017)

Proceedings of Equadiff 14

In this paper, we present a numerical homogenization scheme for indefinite, timeharmonic Maxwell’s equations involving potentially rough (rapidly oscillating) coefficients. The method involves an H(curl)-stable, quasi-local operator, which allows for a correction of coarse finite element functions such that order optimal (w.r.t. the mesh size) error estimates are obtained. To that end, we extend the procedure of [D. Gallistl, P. Henning, B. Verfürth, Numerical homogenization for H(curl)-problems,...

Numerical homogenization of well singularities in the flow transport through heterogeneous porous media: fully discrete scheme

Meiqun Jiang, Xingye Yue (2007)

ESAIM: Mathematical Modelling and Numerical Analysis

Motivated by well-driven flow transport in porous media, Chen and Yue proposed a numerical homogenization method for Green function [Multiscale Model. Simul.1 (2003) 260–303]. In that paper, the authors focused on the well pore pressure, so the local error analysis in maximum norm was presented. As a continuation, we will consider a fully discrete scheme and its multiscale error analysis on the velocity field.

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