Skip Navigation


IMA Journal of Numerical Analysis Advance Access originally published online on November 23, 2006
IMA Journal of Numerical Analysis 2007 27(3):529-549; doi:10.1093/imanum/drl029
This Article
Right arrow Full Text (PDF)
Right arrow All Versions of this Article:
27/3/529    most recent
drl029v1
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by Sinha, R. K.
Right arrow Articles by Deka, B.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

© The author 2006. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

An unfitted finite-element method for elliptic and parabolic interface problems

Rajen Kumar Sinha{dagger}

Department of Mathematics, Indian Institute of Technology Guwahati, Guwahati-781039, India

Bhupen Deka

Department of Mathematics, Assam University, Silchar-788011, India

{dagger} Email: rajen{at}iitg.ernet.in

Received on 20 July 2004. Revised on 15 July 2005.


  Abstract

A finite-element discretization, independent of the location of the interface, is proposed and analysed for linear elliptic and parabolic interface problems. We establish error estimates of optimal order in the H1-norm and almost optimal order in the L2-norm for elliptic interface problems. An extension to parabolic interface problems is also discussed and an optimal error estimate in the L2(0, T;H1({Omega}))-norm and an almost optimal order estimate in the L2(0, T;L2({Omega}))-norm are derived for the spatially discrete scheme. A fully discrete scheme based on the backward Euler method is analysed and an optimal order error estimate in the L2(0, T;H1({Omega}))-norm is derived. The interfaces are assumed to be of arbitrary shape and smooth for our purpose.

Key Words: elliptic and parabolic interface problems; an unfitted finite-element method; spatially discrete and fully discrete schemes; error estimates


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?




Disclaimer: Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department.