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:
    non sort: The
    title: Mathematical Theory of Finite Element Methods
  name:
    name part: Brenner, Susanne C.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: Scott, L. Ridgway.
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: xxu
    date issued: 2008
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XVIII, 400 p. online resource.
  abstract: This book develops the basic mathematical theory of the finite element method, the most widely used technique for engineering design and analysis. The third edition contains four new sections: the BDDC domain decomposition preconditioner, convergence analysis of an adaptive algorithm, interior penalty methods and Poincara\'e-Friedrichs inequalities for piecewise W^1_p functions. New exercises have also been added throughout. The initial chapter provides an introducton to the entire subject, developed in the one-dimensional case. Four subsequent chapters develop the basic theory in the multidimensional case, and a fifth chapter presents basic applications of this theory. Subsequent chapters provide an introduction to: - multigrid methods and domain decomposition methods - mixed methods with applications to elasticity and fluid mechanics - iterated penalty and augmented Lagrangian methods - variational "crimes" including nonconforming and isoparametric methods, numerical integration and interior penalty methods - error estimates in the maximum norm with applications to nonlinear problems - error estimators, adaptive meshes and convergence analysis of an adaptive algorithm - Banach-space operator-interpolation techniques The book has proved useful to mathematicians as well as engineers and physical scientists. It can be used for a course that provides an introduction to basic functional analysis, approximation theory and numerical analysis, while building upon and applying basic techniques of real variable theory. It can also be used for courses that emphasize physical applications or algorithmic efficiency. Reviews of earlier editions: "This book represents an important contribution to the mathematical literature of finite elements. It is both a well-done text and a good reference." (Mathematical Reviews, 1995) "This is an excellent, though demanding, introduction to key mathematical topics in the finite element method, and at the same time a valuable reference and so…
  table of contents: Basic Concepts -- Sobolev Spaces -- Variational Formulation of Elliptic Boundary Value Problems -- The Construction of a Finite Element Space -- Polynomial Approximation Theory in Sobolev Spaces -- n-Dimensional Variational Problems -- Finite Element Multigrid Methods -- Additive Schwarz Preconditioners -- Max—norm Estimates -- Adaptive Meshes -- Variational Crimes -- Applications to Planar Elasticity -- Mixed Methods -- Iterative Techniques for Mixed Methods -- Applications of Operator-Interpolation Theory.
  note: by Susanne C. Brenner, L. Ridgway Scott.
  subject:
    topic: Mathematics
  subject:
    topic: Functional analysis
  subject:
    topic: Applied mathematics
  subject:
    topic: Engineering mathematics
  subject:
    topic: Computer mathematics
  subject:
    topic: Computational intelligence
  subject:
    topic: Mechanics
  subject:
    topic: Mechanics, Applied
  subject:
    topic: Mathematics
  subject:
    topic: Applications of Mathematics
  subject:
    topic: Computational Mathematics and Numerical Analysis
  subject:
    topic: Computational Intelligence
  subject:
    topic: Theoretical and Applied Mechanics
  subject:
    topic: Functional Analysis
  classification: T57-57.97
  classification: 519
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Texts in Applied Mathematics, 15
  identifier: 9780387759340
  identifier: http://dx.doi.org/10.1007/978-0-387-75934-0
  record info:
    record creation date: 100301
    record change date: 20151204184248.0
    record identifier: 978-0-387-75934-0