Identification of the thermal conductivity and heat capacity in unsteady nonlinear heat conduction problems using the boundary element method
type: Item
instance of: scholarly article
title: Identification of the thermal conductivity and heat capacity in unsteady nonlinear heat conduction problems using the boundary element method
zbMATH Open document ID: 0874.65070
author: L. Elliott
author: Daniel Lesnic
author: Derek B. Ingham
published in: Journal of Computational Physics
publication date: 1997-11-10T00:00:00Z
review text: The authors investigate the simultaneous estimation of the temperature-dependent conductivity and heat capacity starting from boundary and initial data supplemented by interior temperature measurements. The unknown temperature solution and unspecified boundary values are required. The mathematical formulation is based on a one-dimensional plane time-dependent nonlinear parabolic initial-boundary value problem of the Dirichlet type. The solution of the direct problem is initiated via a Kirchhoff transformation followed by a boundary element time-marching technique. The inverse problem is approached via a boundary element method employed in an iterative procedure requiring the minimization of a nonlinear least squares functional. Test examples are considered to illustrate the applicability and feasibility of the method.
Mathematics Subject Classification ID: 65M30
Mathematics Subject Classification ID: 80A20
Mathematics Subject Classification ID: 35K55
Mathematics Subject Classification ID: 35R30
Mathematics Subject Classification ID: 65M70
zbMATH DE Number: 937214
zbMATH Keywords: nonlinear heat conduction
zbMATH Keywords: numerical examples
zbMATH Keywords: nonlinear parabolic initial-boundary value problem
zbMATH Keywords: time-marching technique
zbMATH Keywords: inverse problem
zbMATH Keywords: boundary element method
zbMATH Keywords: nonlinear least squares
reviewed by: Nikolai L. Vulchanov
MaRDI profile type: Publication
full work available at URL: jcph.1996.0146
OpenAlex ID: W2084914400
DOI: 10.1006/JCPH.1996.0146
description: scientific article; zbMATH DE number 937214