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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...
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...
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,...
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.
The paper deals with the analysis and numerical study of the domain decomposition based preconditioner for algebraic systems arising from the discontinuous Galerkin (DG) discretization of the linear elliptic problems. We introduce the DG discretization of the model problem and present the spectral -bound of the corresponding linear algebraic systems. Moreover, we present the two-level additive Schwarz preconditioner together with the theoretical result related to the estimate of the condition number....
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