https://doi.org/10.1051/epjconf/202022602007
Construction of Multivariate Interpolation Hermite Polynomials for Finite Element Method
1
Joint Institute for Nuclear Research,
Dubna,
Russia
2
Peoples’ Friendship University of Russia (RUDN University),
Moscow,
Russia
3
Institute of Mathematics and Digital Technologies, Mongolian Academy of Sciences,
Ulaanbaatar,
Mongolia
4
Saratov State University,
Saratov,
Russia
5
Institute of Physics, University of M. Curie-Skłodowska,
Lublin,
Poland
6
Institute of Nuclear Physics,
Almaty,
Kazakhstan
7
Ho Chi Minh city University of Education,
Ho Chi Minh city,
Vietnam
★ e-mail: gooseff@jinr.ru
★★ e-mail: chuka@jinr.ru
★★★ e-mail: vinitsky@theor.jinr.ru
Published online: 20 January 2020
A new algorithm for constructing multivariate interpolation Hermite polynomials in analytical form in a multidimensional hypercube is presented. These polynomials are determined from a specially constructed set of values of the polynomials themselves and their partial derivatives with continuous derivatives up to a given order on the boundaries of the finite elements. The effciency of the finite element schemes, algor thms and programs is demonstrated by solving the Helmholtz problem for a cube.
© The Authors, published by EDP Sciences, 2020
This is an Open Access article distributed under the terms of the Creative Commons Attribution License 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
