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

Convergence analysis of finite element methods for h(curl)-elliptic interface problems

by R. Hiptmair and J.-Z. Li and J. Zou

(Report number 2009-04)

Abstract
In this article we analyse a finite element method for solving H(curl;\Omega)-elliptic interface problems in general three-dimensional polyhedral domains with smooth material interfaces. The continuous problems are discretized by means of the first family of lowest order Nédélec H(curl;\Omega)-conforming finite elements on a family of tetrahedral meshes which resolve the smooth interface in the sense of sufficient approximation in terms of a parameter \delta that quantifies the mismatch between the smooth interface and the triangulation. Optimal error estimates in the H(curl;\Omega) norm are obtained for the first time. The analysis is based on a so-called \delta-strip argument, a new extension theorem for H1(curl)-functions across smooth interfaces, a novel non standard interface-aware interpolation operator, and a perturbation argument for degrees of freedomforH(curl; Omega)-conforming finite elements. Numerical tests are presented to verify the theoretical predictions and confirm the optimal order convergence of the numerical solution.

Keywords: H(curl;\Omega)-elliptic interface problems, finite element methods, Nédélec's edge elements, convergence analysis

@Techreport{HLZ09_66,
  author = {R. Hiptmair and J.-Z. Li and J. Zou},
  title = {Convergence analysis of finite element methods for h(curl)-elliptic interface problems},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2009-04},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2009/2009-04.pdf },
  year = {2009}
}

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).