Sparse second moment analysis for elliptic problems in stochastic domains
type: Item
instance of: scholarly article
title: Sparse second moment analysis for elliptic problems in stochastic domains
zbMATH Open document ID: 1146.65007
author: H. Harbrecht
author: Reinhold Schneider
author: Christoph Schwab
published in: Numerische Mathematik
publication date: 2008-06-17T00:00:00Z
review text: The authors consider the Dirichlet problem for the Poisson equation \[ -\Delta u_{\varepsilon}(\omega)=f\text{ in\;}D_{\varepsilon}(\omega ),\;u_{\varepsilon}(\omega)=g\text{ on }\partial D_{\varepsilon}(\omega), \] where \(D_{\varepsilon}(\omega)\) is a small random perturbation of a domain \(D\subset\mathbb{R}^{n},\;n=2,3.\) They develop a deterministic second moment analysis of the random solution and propose a fast wavelet based algorithm to approximate its mean and correlation function. Some numerical experiments are presented.
reviewed by: Grigori N. Milstein
Mathematics Subject Classification ID: 65C30
Mathematics Subject Classification ID: 35R60
Mathematics Subject Classification ID: 65N38
Mathematics Subject Classification ID: 60H15
Mathematics Subject Classification ID: 60H35
Mathematics Subject Classification ID: 65T60
zbMATH DE Number: 5288752
zbMATH Keywords: Poisson equation
zbMATH Keywords: Dirichlet problem
zbMATH Keywords: random perturbation of domain
zbMATH Keywords: second moment analysis
MaRDI profile type: Publication
full work available at URL: s00211-008-0147-9
OpenAlex ID: W1985681033
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DOI: 10.1007/S00211-008-0147-9
description: scientific article; zbMATH DE number 5288752