Superapproximation properties of the interpolation operator of projection type and applications

Tie Zhang, Yanping Lin, R. J. Tait

Research output: Journal article publicationJournal articleAcademic researchpeer-review

Abstract

Some superapproximation and ultra-approximation properties in function, gradient and two-order derivative approximations are shown for the interpolation operator of projection type on two-dimensional domain. Then, we consider the Ritz projection and Ritz-Volterra projection on finite element spaces, and by means of the superapproximation elementary estimates and Green function methods, derive the superconvergence and ultraconvergence error estimates for both projections, which are also the finite element approximation solutions of the elliptic problems and the Sobolev equations, respectively.
Original languageEnglish
Pages (from-to)277-288
Number of pages12
JournalJournal of Computational Mathematics
Volume20
Issue number3
Publication statusPublished - 1 May 2002
Externally publishedYes

Keywords

  • Finite element
  • Interpolation operator of projection type
  • Superconvergence

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics
  • Computational Mathematics

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