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mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Optimal order preconditioners for mixed and nonconforming finite element approximations of elliptic problems with anisotropy
  name:
    name part: Maliassov, Serguei
    name part: 1964-
    role:
      role term: creator
  type of resource: text
  genre: bibliography
  origin info:
    place:
      place term: xx
    date issued: 1996
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: print
    extent: xi, 187 leaves : illustrations ; 28 cm.
  abstract: The general area of this thesis is preconditioning techniques for mixed and nonconforming finite element approximations of elliptic boundary value problems. A special emphasis is placed on problems in three dimensions with possibly large anisotropy in the coefficients of the PDE's along with large jumps in the coefficients across the interfaces separating subregions. The optimal preconditioners developed exploit the techniques of domain decomposition methods, algebraic substructuring, and multigrid methods. As a result, the proposed iterative processes converge with rates independent of the mesh size, the jumps of the coefficients, and the ratio of anisotropy. Using an equivalence between nonconforming finite element methods and hybridmixed methods the iterative methods constructed for algebraic systems with symmetric positive definite matrices are extended to saddle-point problems which arise from mixed finite element approximations. A new construction of iterative methods for nonconforming approximations of elliptic PDE's on nonmatching grids is proposed. The computational domain is considered as a union of nonintersecting subdomains. In each subdomain the grid is constructed in accordance with its own coordinate system using the main directions of anisotropy. The original elliptic problem is posed as a problem with Lagrange multipliers at the interface between the subdomains, which ensure the continuity conditions of the solution. A mortar finite element subspace is constructed in the space of Lagrange multipliers, which results in algebraic systems of a saddle-point type. Based on the technique of domain decomposition and fictitious components methods conditioners for the algebraic systems arising in the a construction of block diagonal pre mortar finite element method is developed. The fictitious components method is used to precondition subdomain problems, whil interface problems are preconditioned by an innere the Chebyshev iterative procedure. It is shown th…
  note: by Serguei Maliassov.
  note: Vita.
  note: "Major Subject: Mathematics".
  note: Issued also on microfiche from University Microfilms Inc.
  note: Includes bibliographical references.
  note: Ph. D. Texas A&M University 1996.
  subject:
    topic: Major mathematics
  identifier: 96-34804 UMI
  identifier: http://proxy.library.tamu.edu/login
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    location:
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  record info:
    record content source: TXA
    record creation date: 970305
    record change date: 20190325093243.0
    record identifier: in00001336307