THE CONSTRUCTION of schemes of the finite-element method of an arbitrary order of accuracy for second-order elliptic equations in arbitrary sufficiently smooth regions is accomplished in such a way that they are spectrally equivalent to the simplest finite difference approximations of the Laplace equation on a uniform orthogonal mesh. This enables us to construct efficient iterative methods for solving these schemes. Iterative methods on sequences of discharging networks, leading to optimal-order estimates of the number of arithmetic operations are also considered. The results obtained lead to the development of economy of schemes of high orders of accuracy.

Original languageEnglish
Pages (from-to)109-129
Number of pages21
JournalUSSR Computational Mathematics and Mathematical Physics
Volume17
Issue number5
DOIs
StatePublished - 1977

    Scopus subject areas

  • Engineering(all)

ID: 86586899