Adaptive mesh refinement for hyperbolic partial differential equations

Marsha J. Berger, Joseph Oliger

Research output: Contribution to journalArticle

Abstract

An adaptive method based on the idea of multiple component grids for the solution of hyperbolic partial differential equations using finite difference techniques is presented. Based upon Richardson-type estimates of the truncation error, refined grids are created or existing ones removed to attain a given accuracy for a minimum amount of work. The approach is recursive in that fine grids can contain even finer grids. The grids with finer mesh width in space also have a smaller mesh width in time, making this a mesh refinement algorithm in time and space. We present the algorithm, error estimation procedure, and the data structures, and conclude with numerical examples in one and two space dimensions.

Original languageEnglish (US)
Pages (from-to)484-512
Number of pages29
JournalJournal of Computational Physics
Volume53
Issue number3
DOIs
StatePublished - Mar 1984

ASJC Scopus subject areas

  • Numerical Analysis
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)
  • Physics and Astronomy(all)
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics

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