High dimensional finite elements for elliptic problems with multiple scales and stochastic data

Fuente: arXiv
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Auteur principal: Schwab, Christoph
Format: Preprint
Publié: 2003
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author Schwab, Christoph
author_facet Schwab, Christoph
contents Multiple scale homogenization problems are reduced to single scale problems in higher dimension. It is shown that sparse tensor product Finite Element Methods (FEM) allow the numerical solution in complexity independent of the dimension and of the length scale. Problems with stochastic input data are reformulated as high dimensional deterministic problems for the statistical moments of the random solution. Sparse tensor product FEM give a deterministic solution algorithm of log-linear complexity for statistical moments.
format Preprint
id arxiv_https___arxiv_org_abs_math_0305007
institution arXiv
publishDate 2003
record_format arxiv
spellingShingle High dimensional finite elements for elliptic problems with multiple scales and stochastic data
Schwab, Christoph
Numerical Analysis
65N30
Multiple scale homogenization problems are reduced to single scale problems in higher dimension. It is shown that sparse tensor product Finite Element Methods (FEM) allow the numerical solution in complexity independent of the dimension and of the length scale. Problems with stochastic input data are reformulated as high dimensional deterministic problems for the statistical moments of the random solution. Sparse tensor product FEM give a deterministic solution algorithm of log-linear complexity for statistical moments.
title High dimensional finite elements for elliptic problems with multiple scales and stochastic data
topic Numerical Analysis
65N30
url https://arxiv.org/abs/math/0305007