rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Generalized Discontinuous Multiscale Methods for Flows in Highly Heterogeneous Porous Media
  name:
    name part: Moon, Minam
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: Lazarov, Raĭcho
    role:
      role term: thesis advisor.
  name:
    name part: Efendiev, Yalchin
    role:
      role term: thesis advisor.
  name:
    name part: Texas A & M University
    role:
      role term: degree granting institution.
  type of resource: text
  genre: bibliography
  origin info:
    place:
      place term: txu
    date issued: 2015
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: remote
    extent: 1 online resource.
  abstract: This dissertation is devoted to the development, study and testing of numerical methods for elliptic and parabolic equations with heterogeneous coefficients. The motivation for this study is to meet the need for fast and robust methods for numerical upscaling and simulation of single and multi-phase fluid flow in highly heterogeneous porous media. We consider the multiscale model reduction technique in the framework of the discontinuous Galerkin (DG) and the hybridizable discontinuous Galerkin (HDG) finite element methods. First, we design multiscale finite element methods for second order elliptic equations by applying the symmetric interior penalty discontinuous Galekin finite element method. We propose two different types of finite element spaces on the coarse mesh within DG framework. The first type of spaces is based on a local spectral problem that uses an interior weighted L²-norm and a boundary weighted L²-norm for computing the mass matrix. The second choice is based on generation of a snapshot space and subsequent selection of a subspace of a reduced dimension. Second, we develop multiscale model reduction methods within the HDG framework. We provide construction of several multiscale finite element spaces (related to the coarse-mesh edges) that guarantee a reasonable approximation on a reduced dimensional space of the numerical traces. In these approaches, we use local snapshot spaces and local spectral decomposition following the concept of Generalized Multiscale Finite Element Methods. We also provide a general framework for systematic construction of multiscale spaces. By using local snapshots we were able to add local features to the solution space and to avoid high dimensional representation of trace spaces. Further, we extend multiscale finite element methods within HDG method to nonlinear and/or time-dependent problems. These extensions demonstrate the potential of the proposed constructions for some advanced and more practical applications. For mo…
  note: by Minam Moon.
  note: "Major Subject: Mathematics"
  note: Includes vita.
  note: Doctor of Philosophy Texas A & M University 2015 http://hdl.handle.net/1969.1/155430
  note: Includes bibliographical references.
  note: Text (Dissertation)
  subject:
    topic: Major Mathematics
  subject:
    topic: Porous media
  subject:
    topic: Multiscale method
  identifier: http://hdl.handle.net/1969.1/155430
  record info:
    record content source: TXA
    record creation date: 160818
    record change date: 20170926142923.0
    record identifier: in00003742576
    language of cataloging:
      language term: eng