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h p -FEM for three-dimensional elastic plates

Monique Dauge, Christoph Schwab (2002)

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

In this work, we analyze hierarchic h p -finite element discretizations of the full, three-dimensional plate problem. Based on two-scale asymptotic expansion of the three-dimensional solution, we give specific mesh design principles for the h p -FEM which allow to resolve the three-dimensional boundary layer profiles at robust, exponential rate. We prove that, as the plate half-thickness ε tends to zero, the h p -discretization is consistent with the three-dimensional solution to any power of ε in the energy...

Homogenization of a singular random one-dimensional PDE

Bogdan Iftimie, Étienne Pardoux, Andrey Piatnitski (2008)

Annales de l'I.H.P. Probabilités et statistiques

This paper deals with the homogenization problem for a one-dimensional parabolic PDE with random stationary mixing coefficients in the presence of a large zero order term. We show that under a proper choice of the scaling factor for the said zero order terms, the family of solutions of the studied problem converges in law, and describe the limit process. It should be noted that the limit dynamics remain random.

hp-FEM for three-dimensional elastic plates

Monique Dauge, Christoph Schwab (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

In this work, we analyze hierarchic hp-finite element discretizations of the full, three-dimensional plate problem. Based on two-scale asymptotic expansion of the three-dimensional solution, we give specific mesh design principles for the hp-FEM which allow to resolve the three-dimensional boundary layer profiles at robust, exponential rate. We prove that, as the plate half-thickness ε tends to zero, the hp-discretization is consistent with the three-dimensional solution to any power of ε in...

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