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

Space-Time adaptive wavelet methods for parabolic evolution equations

by Ch. Schwab and R. Stevenson

(Report number 2008-01)

Abstract
With respect to space-time tensor product wavelet bases, parabolic initial boundary value problems are equivalently formulated as bi-infinite matrix problems. Adaptive wavelet methods are shown to yield sequences of approximate solutions which converge at the optimal rate. In case the spatial domain is of product type, the use of spatial tensor product wavelet bases is proved to overcome the so-called curse of dimensionality, i.e., the reduction of the convergence rate with increasing spatial dimension.

Keywords: Parabolic differential equations, wavelets, adaptivity, optimal computational complexity, best N-term approximation, matrix compression

@Techreport{SS08_68,
  author = {Ch. Schwab and R. Stevenson},
  title = {Space-Time adaptive wavelet methods for parabolic evolution equations},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2008-01},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2008/2008-01.pdf },
  year = {2008}
}

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).