Research reports
Years: 2024 2023 2022 2021 2020 2019 2018 2017 2016 2015 2014 2013 2012 2011 2010 2009 2008 2007 2006 2005 2004 2003 2002 2001 2000 1999 1998 1997 1996 1995 1994 1993 1992 1991
An adaptive finite element method for distributed heat flux reconstruction
by J. Li and J. Xie and J. Zou
(Report number 2010-23)
Abstract
Based on a posteriori error estimates, we propose an adaptive finite element method for a distributed heat flux reconstruction in a stationary heat conductive system, namely recovering the unknown distributed flux on some inaccessible boundary using partial measurement data on other accessible boundaries. A posteriori error estimates are first derived. Efficiency of the derived error estimator is addressed by showing that the error estimator provides upper and lower bounds on the discretization errors of quantities of interest, up to some constants. It is revealed for the first time that the constant of the upper bound depends explicitly on the regularization parameter, which could be essential for employing adaptive techniques to inverse problems. Numerical experiments are presented to show the applicability and efficiency of the proposed adaptive method based on the derived error estimator.
Keywords:
BibTeX@Techreport{LXZ10_428, author = {J. Li and J. Xie and J. Zou}, title = {An adaptive finite element method for distributed heat flux reconstruction}, institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich}, number = {2010-23}, address = {Switzerland}, url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2010/2010-23.pdf }, year = {2010} }
Disclaimer
© Copyright for documents on this server remains with the authors.
Copies of these documents made by electronic or mechanical means including
information storage and retrieval systems, may only be employed for
personal use. The administrators respectfully request that authors
inform them when any paper is published to avoid copyright infringement.
Note that unauthorised copying of copyright material is illegal and may
lead to prosecution. Neither the administrators nor the Seminar for
Applied Mathematics (SAM) accept any liability in this respect.
The most recent version of a SAM report may differ in formatting and style
from published journal version. Do reference the published version if
possible (see SAM
Publications).