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Piecewise Linear Approximation by the Method of Worst Segment Division

Authors
  • Sukiasyan, H. S.1, 2
  • 1 Institute of Mathematics, National Academy of Sciences of the Republic of Armenia, Yerevan, 0019, Armenia , Yerevan (Armenia)
  • 2 National Polytechnic University of Armenia, Yerevan, Armenia , Yerevan (Armenia)
Type
Published Article
Journal
Lobachevskii Journal of Mathematics
Publisher
Pleiades Publishing
Publication Date
Dec 13, 2021
Volume
42
Issue
12
Pages
2969–2979
Identifiers
DOI: 10.1134/S1995080221120325
Source
Springer Nature
Keywords
Disciplines
  • Article
License
Yellow

Abstract

AbstractThe finite element method for numerical solving two-dimensional boundary value problem is based on domain triangulation and piecewise linear approximation. The present paper describes how to minimize the number of triangulation vertices without exceeding the given level of the approximation error. The paper proposes a method for constructing piecewise linear approximations for continuous two-dimensional functions by dividing the ‘‘worst’’ segment. The possibilities of applying the proposed method in solving boundary value problems are investigated. The main theorem gives a sufficient condition on the minimized functional so that the best mesh would be the Delaunay triangulation. An example of a numerical solution of the Maxwell equation of the electromagnetic field using the method of the worst segment division with Delaunay triangulation is given.

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