MATHICSE Technical Report : A priori error for unilateral contact problems with Lagrange multipliers and IsoGeometric Analyis
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In this paper, we propose reduced basis multiscale finite element methods (RB-MsFEM) for elliptic problems with highly oscillating coefficients. The method is based on multiscale finite element methods with local test functions that encode the oscillatory ...
Society for Industrial and Applied Mathematics2015
A new finite element heterogeneous multiscale method (FE-HMM) is proposed for the numerical solution of the wave equation over long times in a rapidly varying medium. Our new FE-HMM-L method captures not only the short-time behavior of the wave field, well ...
We introduce new sufficient conditions for a numerical method to approximate with high order of accuracy the invariant measure of an ergodic system of stochastic differential equations, independently of the weak order of accuracy of the method. We then pre ...
Society for Industrial and Applied Mathematics2014
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We introduce and analyze an efficient numerical homogenization method for a class of nonlinear parabolic problems of monotone type in highly oscillatory media. The new scheme avoids costly Newton iterations and is linear at both the macroscopic and the mic ...
We present a novel method to couple molecular dynamics with finite elements at finite temperatures using spatial filters. The mismatch in the dispersion relations between continuum and atomistic models leads, at finite temperature, to unwanted mesh vibrati ...
In this paper, we develop a nodal discontinuous Galerkin method for solving the time-dependent Maxwell's equations when metamaterials are involved. Both semi- and fully-discrete schemes are constructed. Numerical stability and error estimate are proved for ...
In focusing Kerr media, small- scale filamentation is the major obstacle to imaging at high light intensities. In this article, we experimentally and numerically demonstrate a method based on statistical averaging to reduce the detrimental effects of filam ...
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This review paper collects several results that form part of the theoretical foundation of isogeometric methods. We analyse variational techniques for the numerical resolution of PDEs based on splines or NURBS and we provide optimal approximation and error ...