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

Exponential convergence of simplicial hp-FEM for H ¹-functions with isotropic singularities

by Ch. Schwab

(Report number 2014-15)

Abstract
For functions \(u\in H^1(\Omega)\) in a bounded polyhedron \(\Omega\subset \mathbb{R}^d\), \(d=2,3\), which are analytic in \(\overline{\Omega}\backslash \mathcal{S}\) with point singularities concentrated at the set \(\mathcal{S}\subset \overline{\Omega}\) consisting of a finite number of points in \(\overline{\Omega}\), we prove exponential rates of convergence of \(hp\)-version continuous Galerkin finite element methods on families of regular, simplicial meshes in \(\Omega\). The simplicial meshes are assumed to be geometrically refined towards \(\mathcal{S}\) and to be shape regular, but are otherwise unstructured.

Keywords:

@Techreport{S14_565,
  author = {Ch. Schwab},
  title = {Exponential convergence of simplicial hp-FEM for H ¹-functions with isotropic singularities},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2014-15},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2014/2014-15.pdf },
  year = {2014}
}

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).