Weighted Poincaré inequalities and applications in domain decomposition

Clemens Pechstein, Robert Scheichl

Research output: Chapter in Book/Report/Conference proceedingChapter

14 Citations (Scopus)

Abstract

Poincare´ type inequalities play a central role in the analysis of domain decomposition and multigrid methods for second-order elliptic problems. However, when the coefficient varies within a subdomain or within a coarse grid element, then standard condition number bounds for these methods may be overly pessimistic. In this short note we present new weighted Poincare´ type inequalities for a class of piecewise constant coefficients that lead to sharper bounds independent of any possible large contrasts in the coefficients.
Original languageEnglish
Title of host publicationDomain Decomposition Methods in Science and Engineering XIX
Place of PublicationHeidelberg
PublisherSpringer
Pages197-204
Number of pages8
Volume78
DOIs
Publication statusPublished - 2010

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    Pechstein, C., & Scheichl, R. (2010). Weighted Poincaré inequalities and applications in domain decomposition. In Domain Decomposition Methods in Science and Engineering XIX (Vol. 78, pp. 197-204). Springer. https://doi.org/10.1007/978-3-642-11304-8_21