A Petrov Galerkin finite-element method for interface problems arising in sensitivity computa\-tions
type: Item
instance of: scholarly article
title: A Petrov Galerkin finite-element method for interface problems arising in sensitivity computa\-tions
zbMATH Open document ID: 1087.65078
author: John A. Burns
author: Lisa G. Stanley
author: Tao Lin
publication date: 2006-02-02T00:00:00Z
review text: A discontinuous Petrov Galerkin finite element method is proposed and analyzed to deal with the computation of sensitivity analysis of 1D interface problems. First, to motivate the difficulties arising in the numerical solution of these problems the authors start by introducing a simple example of steady state heat conduction in a thin rod with \( \Omega=[0,1]\) consisting of two materials with the interface at the spatial location \( x=q,\) \(q \in (0,1)\). It is shown that a weak formulation is necessary to capture the discontinuities of the solution and by means of a Petrov Galerkin method with suitable trial functions they are able to establish the existence of a unique solution and to prove the convergence in suitable spaces. Further, the paper presents the results of two numerical examples to show the advantage of the proposed technique over a standard finite element approach because it avoids Gibbs phenomena in the discontinuity of the sensitivity across the interface.
reviewed by: Manuel Calvo
Mathematics Subject Classification ID: 65L60
Mathematics Subject Classification ID: 65L10
Mathematics Subject Classification ID: 34B05
Mathematics Subject Classification ID: 65L20
zbMATH DE Number: 5003108
zbMATH Keywords: 1D Elliptic Interface Problems
zbMATH Keywords: Petrov Galerkin finite elements
zbMATH Keywords: sensitivity analysis
zbMATH Keywords: heat conduction
zbMATH Keywords: convergence
zbMATH Keywords: numerical examples
MaRDI profile type: Publication
full work available at URL: j.camwa.2004.06.037
OpenAlex ID: W1990969382
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DOI: 10.1016/J.CAMWA.2004.06.037
published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 5003108