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: Numerical Models for Differential Problems
  name:
    name part: Quarteroni, Alfio.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: it
    date issued: 2014
    edition: Second Edition.
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XIX, 658 p. online resource.
  abstract: In this text, we introduce the basic concepts for the numerical modelling of partial differential equations. We consider the classical elliptic, parabolic and hyperbolic linear equations, but also the diffusion, transport, and Navier-Stokes equations, as well as equations representing conservation laws, saddle-point problems and optimal control problems. Furthermore, we provide numerous physical examples which underline such equations. We then analyze numerical solution methods based on finite elements, finite differences, finite volumes, spectral methods and domain decomposition methods, and reduced basis methods. In particular, we discuss the algorithmic and computer implementation aspects and provide a number of easy-to-use programs. The text does not require any previous advanced mathematical knowledge of partial differential equations: the absolutely essential concepts are reported in a preliminary chapter. It is therefore suitable for students of bachelor and master courses in scientific disciplines, and recommendable to those researchers in the academic and extra-academic domain who want to approach this interesting branch of applied mathematics.
  table of contents: 1 A brief survey of partial differential equations -- 2 Elements of functional analysis -- 3 Elliptic equations -- 4 The Galerkin finite element method for elliptic problems -- 5 Parabolic equations -- 6 Generation of 1D and 2D grids -- 7 Algorithms for the solution of linear systems -- 8 Elements of finite element programming -- 9 The finite volume method -- 10 Spectral methods -- 11 Discontinuous element methods (DG and mortar) -- 12 Diffusion-transport-reaction equations -- 13 Finite differences for hyperbolic equations -- 14 Finite elements and spectral methods for hyperbolic equations -- 15 Nonlinear hyperbolic problems -- 16 Navier-Stokes equations -- 17 Optimal control of partial differential equations -- 18 Domain decomposition methods -- 19 Reduced basis approximation for parametrized partial differential equations.
  note: by Alfio Quarteroni.
  subject:
    topic: Mathematics
  subject:
    topic: Mathematical analysis
  subject:
    topic: Analysis (Mathematics)
  subject:
    topic: Applied mathematics
  subject:
    topic: Engineering mathematics
  subject:
    topic: Computer mathematics
  subject:
    topic: Numerical analysis
  subject:
    topic: Mathematical models
  subject:
    topic: Mathematics
  subject:
    topic: Mathematics, general
  subject:
    topic: Analysis
  subject:
    topic: Numerical Analysis
  subject:
    topic: Mathematical Modeling and Industrial Mathematics
  subject:
    topic: Applications of Mathematics
  subject:
    topic: Computational Mathematics and Numerical Analysis
  classification: QA1-939
  classification: 510
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: MS&A - Modeling, Simulation and Applications, 8
  identifier: 9788847055223
  identifier: http://dx.doi.org/10.1007/978-88-470-5522-3
  record info:
    record creation date: 140425
    record change date: 20151204165940.0
    record identifier: 978-88-470-5522-3