Error estimates of finite element methods for parameter identifications in elliptic and parabolic systems
type: Item
instance of: scholarly article
title: Error estimates of finite element methods for parameter identifications in elliptic and parabolic systems
zbMATH Open document ID: 1214.35085
author: Jun Zou
author: Lijuan Wang
published in: Discrete and Continuous Dynamical Systems. Series B
publication date: 2011-01-17T00:00:00Z
review text: The purpose of this paper is the identification of a parameter in the elliptic equation \[ -\nabla \cdot (q(x)\nabla u(x))=f(x)\quad \text{in }\Omega \] or in the parabolic equation \[ u_t-\nabla \cdot (q(x)\nabla u)=g(x,t)\quad \text{in }\Omega\times (0,T), \] with Neumann homogeneous boundary conditions and an initial condition for the parabolic problem. The focus of this work is to find both the solution \(u\) and the distributed coefficient \(q\), when some measurement of \(u\) is given. By means of the Tikhonov's regularization, the inverse problem of reconstructing \(q\) may be formulated as a minimization problem. By using piecewise linear finite element approximations to the regularization systems, \(L^2\) and energy-norm error estimates for the approximations of the coefficient \(q\) are established.
reviewed by: Ruxandra Stavre
Mathematics Subject Classification ID: 35R30
Mathematics Subject Classification ID: 65M32
Mathematics Subject Classification ID: 65M15
Mathematics Subject Classification ID: 65N15
Mathematics Subject Classification ID: 65N21
zbMATH DE Number: 5837953
zbMATH Keywords: parameter identification
zbMATH Keywords: Tikhonov regularization
zbMATH Keywords: finite element method
zbMATH Keywords: error estimates
MaRDI profile type: Publication
full work available at URL: dcdsb.2010.14.1641
OpenAlex ID: W2045623154
DOI: 10.3934/DCDSB.2010.14.1641
description: scientific article; zbMATH DE number 5837953