Adaptive finite element methods for the identification of distributed parameters in elliptic equation
type: Item
instance of: scholarly article
title: Adaptive finite element methods for the identification of distributed parameters in elliptic equation
zbMATH Open document ID: 1148.65086
author: Tao Feng
author: Ningning Yan
author: Wenbin Liu
published in: Advances in Computational Mathematics
publication date: 2008-08-20T00:00:00Z
review text: The authors consider the problem of determining the unknown functional coefficient \(q\) in the elliptic equation \[ -\nabla(q(x) \nabla u)=f, \quad x \in \Omega; \quad u=0, \quad x \in \partial \Omega \] by the observation data \(u=z \in L_2(\Omega)\). The domain \(\Omega\) is a bounded open subset of \(\mathbb R^n\) \((n \geq 3)\) with \(\partial \Omega \in C^3\) or \(\Omega\) is a parallelepiped. The original inverse problem is reduced to the variational problem \[ \min_{q \in K} \{ \| u(q)-z\|^2_{L_2(\Omega)}+ \beta \| \nabla q \|^2_{L_2(\Omega)} \}, \] where \(K=\{ q\in W^{1,t}: 0<\alpha \leq q(x) \leq \nu, q|_{\partial \Omega}=q^* \}\), \(t>n\).
reviewed by: Mikhail Yu. Kokurin
Mathematics Subject Classification ID: 65N21
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 35R30
Mathematics Subject Classification ID: 65N30
zbMATH DE Number: 5314283
zbMATH Keywords: parameter identification
zbMATH Keywords: finite element
zbMATH Keywords: least-squares
zbMATH Keywords: Gauss-Newton method
zbMATH Keywords: elliptic equation
zbMATH Keywords: inverse problem
MaRDI profile type: Publication
full work available at URL: s10444-007-9035-6
OpenAlex ID: W2044333097
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DOI: 10.1007/S10444-007-9035-6
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description: scientific article; zbMATH DE number 5314283