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

Neumann-Neumann and FETI preconditioners for hp-approximations on geometrically refined boundary layer meshes in two dimensions

by A. Toselli and X. Vasseur

(Report number 2002-15)

Abstract
We develop and analyze Neumann-Neumann and FETI methods for hp finite element approximations of scalar elliptic problems on geometrically refined boundary layer meshes in two dimensions. These are meshes that are highly anisotropic where the aspect ratio grows exponentially with the polynomial degree. The condition number is independent of the aspect ratio of the mesh and of potentially large jumps on the coefficients. In addition, it only grows polylogarithmically with the polynomial degree, as in the case of p approximations on shape-regular meshes.

Keywords: domain decomposition, preconditioning, hp finite elements, spectral elements, anisotropic meshes

@Techreport{TV02_301,
  author = {A. Toselli and X. Vasseur},
  title = {Neumann-Neumann and FETI preconditioners for hp-approximations on geometrically refined boundary layer meshes in two dimensions},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2002-15},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2002/2002-15.pdf },
  year = {2002}
}

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).