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Symbolic-Numerical Algorithm for Generating Interpolation Multivariate Hermite Polynomials of High-Accuracy Finite Element Method

  • A. A. GusevEmail author
  • V. P. Gerdt
  • O. Chuluunbaatar
  • G. Chuluunbaatar
  • S. I. Vinitsky
  • V. L. Derbov
  • A. Góźdź
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10490)

Abstract

A symbolic-numerical algorithm implemented in Maple for constructing Hermitian finite elements is presented. The basis functions of finite elements are high-order polynomials, determined from a specially constructed set of values of the polynomials themselves, their partial derivatives, and their derivatives along the directions of the normals to the boundaries of finite elements. Such a choice of the polynomials allows us to construct a piecewise polynomial basis continuous across the boundaries of elements together with the derivatives up to a given order, which is used to solve elliptic boundary value problems using the high-accuracy finite element method. The efficiency and the accuracy order of the finite element scheme, algorithm and program are demonstrated by the example of the exactly solvable boundary-value problem for a triangular membrane, depending on the number of finite elements of the partition of the domain and the number of piecewise polynomial basis functions.

Keywords

Hermite interpolation polynomials Boundary-value problem High-accuracy finite element method 

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • A. A. Gusev
    • 1
    Email author
  • V. P. Gerdt
    • 1
    • 2
  • O. Chuluunbaatar
    • 1
    • 3
  • G. Chuluunbaatar
    • 1
  • S. I. Vinitsky
    • 1
    • 2
  • V. L. Derbov
    • 4
  • A. Góźdź
    • 5
  1. 1.Joint Institute for Nuclear ResearchDubnaRussia
  2. 2.RUDN UniversityMoscowRussia
  3. 3.Institute of MathematicsNational University of MongoliaUlaanbaatarMongolia
  4. 4.N.G. Chernyshevsky Saratov National Research State UniversitySaratovRussia
  5. 5.Institute of PhysicsUniversity of M. Curie-SkłodowskaLublinPoland

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