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. © 2017, Springer International Publishing AG.

Authors

Gusev A.A.^{1}
,
Gerdt V.P.
^{1,}
^{2}
,
Chuluunbaatar O.
^{1,}
^{3}
,
Chuluunbaatar G.^{1}
,
Vinitsky S.I.
^{1,}
^{2}
,
Derbov V.L.^{4}
,
Góźdź A.^{5}

Language

English

Pages

134-150

Status

Published

Volume

10490 LNCS

Year

2017

Organizations

^{1}Joint Institute for Nuclear Research, Dubna, Russian Federation^{2}RUDN University, 6 Miklukho-Maklaya St., Moscow, 117198, Russian Federation^{3}Institute of Mathematics, National University of Mongolia, Ulaanbaatar, Mongolia^{4}N.G. Chernyshevsky Saratov National Research State University, Saratov, Russian Federation^{5}Institute of Physics, University of M. Curie-Skłodowska, Lublin, Poland

Keywords

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

Date of creation

19.10.2018

Date of change

19.10.2018

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