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: Partial differential equations
  title info:
    title: Journal of computational and applied mathematics
  name:
    name part: Sloan, D. (David)
  name:
    name part: Süli, Endre
    name part: 1956-
  name:
    name part: Vandewalle, Stefan
    name part: 1962-
  name:
    name part: ScienceDirect (Online service)
  type of resource: text
  genre: bibliography
  genre: Electronic books.
  origin info:
    place:
      place term: ne
    place:
      place term: Amsterdam
    place:
      place term: New York
    publisher: Elsevier
    date issued: 2001
    edition: 1st ed.
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: remote
    extent: 1 online resource (xi, 466 pages) : illustrations
  abstract: $81.1 x$a /homepage/sac/cam/na2000/index.html7-Volume Set now available at special set price ! Over the second half of the 20th century the subject area loosely referred to as numerical analysis of partial differential equations (PDEs) has undergone unprecedented development. At its practical end, the vigorous growth and steady diversification of the field were stimulated by the demand for accurate and reliable tools for computational modelling in physical sciences and engineering, and by the rapid development of computer hardware and architecture. At the more theoretical end, the analytical insight into the underlying stability and accuracy properties of computational algorithms for PDEs was deepened by building upon recent progress in mathematical analysis and in the theory of PDEs. To embark on a comprehensive review of the field of numerical analysis of partial differential equations within a single volume of this journal would have been an impossible task. Indeed, the 16 contributions included here, by some of the foremost world authorities in the subject, represent only a small sample of the major developments. We hope that these articles will, nevertheless, provide the reader with a stimulating glimpse into this diverse, exciting and important field. The opening paper by Thomée reviews the history of numerical analysis of PDEs, starting with the 1928 paper by Courant, Friedrichs and Lewy on the solution of problems of mathematical physics by means of finite differences. This excellent survey takes the reader through the development of finite differences for elliptic problems from the 1930s, and the intense study of finite differences for general initial value problems during the 1950s and 1960s. The formulation of the concept of stability is explored in the Lax equivalence theorem and the Kreiss matrix lemmas. Reference is made to the introduction of the finite element method by structural engineers, and a description is given of the subsequent development an…
  abstract: The paper also describes moving finite volume and discrete l2 least-squares methods. Huang and Russell review a class of moving mesh algorithms based upon a moving mesh partial differential equation (MMPDE). The authors are leading players in this research area, and the paper is largely a review of their own work in developing viable MMPDEs and efficient solution strategies. The remaining three papers in this special issue are by Budd and Piggott, Ewing and Wang and van der Houwen and Sommeijer. The paper by Budd and Piggott on geometric integration is a survey of adaptive methods and scaling invariance for discretisations of ordinary and partial differential equations. The authors have succeeded in presenting a readable account of material that combines abstract concepts and practical scientific computing. Geometric integration is a new and rapidly growing area which deals with the derivation of numerical methods for differential equations that incorporate qualitative information in their structure. Qualitative features that may be present in PDEs might include symmetries, asymptotics, invariants or orderings and the objective is to take these properties into account in deriving discretisations. The paper by Ewing and Wang gives a brief summary of numerical methods for advection-dominated PDEs. Models arising in porous medium fluid flow are presented to motivate the study of the advection-dominated flows. The numerical methods reviewed are applicable not only to porous medium flow problems but second-order PDEs with dominant hyperbolic behaviour in general. The paper by van der Houwen and Sommeijer deals with approximate factorisation for time-dependent PDEs. The paper begins with some historical notes and it procee.
  table of contents: Front Cover; Partial Differential Equations; Copyright Page; Table of Contents; Preface; Chapter 1. From finite differences to finite elements. A short history of numerical analysis of partial differential equations; Abstract; 0. Introduction; 1. The Courant-Friedrichs-Lewy paper; 2. Finite difference methods for elliptic problems; 3. Finite difference methods for initial value problems; 4. Finite differences for mixed initial-boundary value problems; 5. Finite element methods for elliptic problems; 6. Finite element methods for evolution equations
  table of contents: 7. Some other classes of approximation methods8. Numerical linear algebra for elliptic problems; References; Survey articles and books; Chapter 2. Orthogonal spline collocation methods for partial differential equations; Abstract; 1. Introduction; 2. Problems in one space variable; 3. Elliptic boundary value problems; 4. Time-dependent problems; 5. Modified spline collocation methods; Acknowledgements; References; Chapter 3. Spectral methods for hyperbolic problems; Abstract; 1. Introduction; 2. Modes and nodes; 3. Approximation results; 4. Collocation approximations of hyperbolic problems
  table of contents: 5. Stability results for hyperbolic problems6. Convergence results for nonlinear hyperbolic problems; 7. Multi-domain methods; 8. A few applications and concluding remarks; References; Chapter 4. Wavelet methods for PDEs -- some recent developments; Abstract; 1. Introduction; 2. Some preliminary comments; 3. The key features; 4. Well-posedness in Euclidean metric; 5. Near sparsity of matrix representations; 6. Adaptive wavelet schemes; 7. Nonlinear problems; 8. About the tools -- some basic concepts; 9. Construction of wavelets on bounded domains
  table of contents: 10. Applications in conventional discretizations11. Concluding remarks; References; Chapter 5. Devising discontinuous Galerkin methods for non-linear hyperbolic conservation laws; Abstract; 1. Introduction; 2. The main difficulty: the loss of well-posedness; 3. Devising discontinuous Galerkin methods: heuristics; 4. The RKDG method; 5. Concluding remarks; Acknowledgements; References; Chapter 6. Adaptive Galerkin finite element methods for partial differential equations; Abstract; 1. Introduction; 2. A general paradigm for a posteriori error estimation
  table of contents: 3. Evaluation of the a posteriori error estimates4. Algorithmic aspects of mesh adaptation; 5. A nested solution approach; 6. Applications to model problems; 7. Conclusion and outlook; Acknowledgements; References; Chapter 7. The p and hp finite element method for problems on thin domains; Abstract; 1. Introduction; 2. h, p and hp finite element spaces; 3. Control of modeling error; 4. Approximation of singularities; 5. Resolution of boundary layers; 6. The problem of locking; References; Chapter 8. Efficient preconditioning of the linearized Navier-Stokes equations for incompressible flow
  note: edited by D. Sloan, E. Süli, S. Vandewalle.
  note: "[Published also as] Journal of computational and applied mathematics, volume 128, numbers 1-2, 1 March 2001"--Page [vii]
  note: Includes bibliographical references and index.
  note: English.
  subject:
    topic: Differential equations, Partial
  subject:
    topic: Équations aux dérivées partielles
  subject:
    topic: MATHEMATICS
    topic: Differential Equations
    topic: Partial
  subject:
    topic: Differential equations, Partial
  classification: QA377 .P294 2001eb
  classification: 515/.353
  related item:
    title info:
      title: Partial differential equations
    origin info:
      publisher: Amsterdam ; New York : Elsevier, 2001
      edition: 1st ed.
    identifier: (DLC) 2002282448
    identifier: (OCoLC)49860053
  related item:
    title info:
      title: Numerical analysis 2000 ; v. 7
  identifier: 9780080929569
  identifier: 0080929567
  identifier: 0444506160
  identifier: 9780444506160
  identifier: 0444505997
  identifier: 9780444505996
  identifier: http://proxy.library.tamu.edu/login
  record info:
    record content source: OPELS
    record creation date: 130411
    record change date: 20260326194330.9
    record identifier: in00005752004
    language of cataloging:
      language term: eng