Discretization methods

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

Research output: Contribution to journalArticle

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)
Pages (from-to)59-108
Number of pages50
JournalMathematics in Science and Engineering
Volume213
Issue numberC
DOIs
StatePublished - 2008
Externally publishedYes

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Discretization Method
Partial differential equations
Discretization
Integral equations
Mathematical operators
Partial differential equation
Irregular Grids
Grid
Adaptive Grid
Geometry
Approximation of Functions
Integral Equations
Approximate Solution
Choose
Space-time
Subspace
Formulation
Operator
Form

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)

Cite this

Discretization methods. / Brio, Moysey; Webb, G. M.; Zakharian, A. R.

In: Mathematics in Science and Engineering, Vol. 213, No. C, 2008, p. 59-108.

Research output: Contribution to journalArticle

Brio, Moysey ; Webb, G. M. ; Zakharian, A. R. / Discretization methods. In: Mathematics in Science and Engineering. 2008 ; Vol. 213, No. C. pp. 59-108.
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