Inf-sup estimates for the Stokes problem in a periodic channel Metadata

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Title

  • Main Title Inf-sup estimates for the Stokes problem in a periodic channel

Creator

  • Author: Wilkening, Jon
    Creator Type: Personal

Contributor

  • Sponsor: Lawrence Berkeley National Laboratory. Computational Research Division.
    Contributor Type: Organization

Publisher

  • Name: Lawrence Berkeley National Laboratory
    Place of Publication: Berkeley, California
    Additional Info: Ernest Orlando Lawrence Berkeley National Laboratory, Berkeley, CA (United States)

Date

  • Creation: 2008-12-10

Language

  • English

Description

  • Content Description: We derive estimates of the Babuska-Brezzi inf-sup constant {beta} for two-dimensional incompressible flow in a periodic channel with one flat boundary and the other given by a periodic, Lipschitz continuous function h. If h is a constant function (so the domain is rectangular), we show that periodicity in one direction but not the other leads to an interesting connection between {beta} and the unitary operator mapping the Fourier sine coefficients of a function to its Fourier cosine coefficients. We exploit this connection to determine the dependence of {beta} on the aspect ratio of the rectangle. We then show how to transfer this result to the case that h is C{sup 1,1} or even C{sup 0,1} by a change of variables. We avoid non-constructive theorems of functional analysis in order to explicitly exhibit the dependence of {beta} on features of the geometry such as the aspect ratio, the maximum slope, and the minimum gap thickness (if h passes near the substrate). We give an example to show that our estimates are optimal in their dependence on the minimum gap thickness in the C{sup 1,1} case, and nearly optimal in the Lipschitz case.

Subject

  • Keyword: Periodicity
  • Keyword: Geometry
  • Keyword: Thickness
  • Keyword: Incompressible Flow
  • Keyword: Aspect Ratio
  • STI Subject Categories: 97
  • Keyword: Functional Analysis

Source

  • Journal Name: SIAM Journal on Mathematical Analysis

Collection

  • Name: Office of Scientific & Technical Information Technical Reports
    Code: OSTI

Institution

  • Name: UNT Libraries Government Documents Department
    Code: UNTGD

Resource Type

  • Article

Format

  • Text

Identifier

  • Report No.: LBNL-1295E
  • Grant Number: DE-AC02-05CH11231
  • Office of Scientific & Technical Information Report Number: 944571
  • Archival Resource Key: ark:/67531/metadc900046