A discrete commutator theory for the consistency and phase error analysis of semi-discrete C0 finite element approximations to the linear transport equation

Travis Thompson

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

A novel method, based on a discrete commutator, for the analysis of consistency error and phase relations for semi-discrete continuous finite element approximation of the one-way wave equation is presented. The technique generalizes to arbitrary dimension, accommodates the use of compatible quadratures, does not require the use of complex calculations, is applicable on non-uniform mesh geometries, and is especially useful when conventional Taylor series or Fourier approaches are intractable. Following the theory the analysis method is demonstrated for several test cases.
Original languageEnglish (US)
Pages (from-to)229-248
Number of pages20
JournalJournal of Computational and Applied Mathematics
Volume303
DOIs
StatePublished - Sep 2016
Externally publishedYes

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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