Discretization methods

M. Brio, G. M. Webb, A. R. Zakharian

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

Discretization of partial differential equations (PDEs) is based on the theory of function approximation, with several key choices to be made: an integral equation formulation, or approximate solution operator; the type of discretization, defined by the function subspace in which the solution is approximated; the choice of grids, e.g. regular versus irregular grids to conform to the geometry, or static versus solution adaptive grids. We explore some of the common approaches to the choice of form of the PDE and the space-time discretization, leaving discussion of the grids for a later chapter. The goal is to introduce the reader to various forms of discretization and to illustrate the numerical performance of different methods. In particular, we will address how to choose a method that is accurate, robust and efficient for the problem at hand.

Original languageEnglish (US)
Title of host publicationMathematics in Science and Engineering
PublisherElsevier
Pages59-108
Number of pages50
EditionC
DOIs
StatePublished - Jan 1 2010
Externally publishedYes

Publication series

NameMathematics in Science and Engineering
NumberC
Volume213
ISSN (Print)0076-5392

Keywords

  • Alternating-Direction-Implicit method
  • Compact finite-differences
  • Finite-differences
  • Lagrangian interpolation
  • Method of weighted residuals
  • Spectral differentiation

ASJC Scopus subject areas

  • Mathematics(all)
  • Engineering(all)

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  • Cite this

    Brio, M., Webb, G. M., & Zakharian, A. R. (2010). Discretization methods. In Mathematics in Science and Engineering (C ed., pp. 59-108). (Mathematics in Science and Engineering; Vol. 213, No. C). Elsevier. https://doi.org/10.1016/S0076-5392(10)21307-3