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: Symmetric Discontinuous Galerkin Methods for 1-D Waves
    sub title: Fourier Analysis, Propagation, Observability and Applications
  name:
    name part: Marica, Aurora.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: Zuazua, Enrique.
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: xxu
    date issued: 2014
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XVI, 104 p. 18 illus. in color. online resource.
  abstract: This work describes the propagation properties of the so-called symmetric interior penalty discontinuous Galerkin (SIPG) approximations of the 1-d wave equation. This is done by means of linear approximations on uniform meshes. First, a careful Fourier analysis is constructed, highlighting the coexistence of two Fourier spectral branches or spectral diagrams (physical and spurious) related to the two components of the numerical solution (averages and jumps). Efficient filtering mechanisms are also developed by means of techniques previously proved to be appropriate for classical schemes like finite differences or P1-classical finite elements. In particular, the work presents a proof that the uniform observability property is recovered uniformly by considering initial data with null jumps and averages given by a bi-grid filtering algorithm. Finally, the book explains how these results can be extended to other more sophisticated conforming and non-conforming finite element methods, in particular to quadratic finite elements, local discontinuous Galerkin methods and a version of the SIPG method adding penalization on the normal derivatives of the numerical solution at the grid points. This work is the first publication to contain a rigorous analysis of the discontinuous Galerkin methods for wave control problems. It will be of interest to a range of researchers specializing in wave approximations.
  table of contents: 1. Preliminaries -- 2. Discontinuous Galerkin approximations and main results -- 3. Bibliographical notes -- 4. Fourier analysis of the DG methods -- 5. Non-uniform observability for DG approximations of waves -- 6. Filtering mechanisms -- 7. Extensions to other numerical approximation schemes -- 8. Comments and open problems -- A technical proof -- References.
  note: by Aurora Marica, Enrique Zuazua.
  subject:
    topic: Mathematics
  subject:
    topic: Approximation theory
  subject:
    topic: Fourier analysis
  subject:
    topic: Partial differential equations
  subject:
    topic: Applied mathematics
  subject:
    topic: Engineering mathematics
  subject:
    topic: Algorithms
  subject:
    topic: Numerical analysis
  subject:
    topic: Mathematics
  subject:
    topic: Numerical Analysis
  subject:
    topic: Fourier Analysis
  subject:
    topic: Approximations and Expansions
  subject:
    topic: Partial Differential Equations
  subject:
    topic: Algorithms
  subject:
    topic: Applications of Mathematics
  classification: QA297-299.4
  classification: 518
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: SpringerBriefs in Mathematics
  identifier: 9781461458111
  identifier: http://dx.doi.org/10.1007/978-1-4614-5811-1
  record info:
    record creation date: 140310
    record change date: 20151124021227.0
    record identifier: 978-1-4614-5811-1