Construction of Multivariate Interpolation Hermite Polynomials for Finite Element Method
Joint Institute for Nuclear Research,
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
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
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