Научная электронная библиотека ULRICH'S Periodicals Directory

Сибирский государственный университет
науки и технологий имени академика М.Ф. Решетнева

Сибирский аэрокосмический журнал
ISSN 2712-8970 (Print) ISSN 2782-5760 (on-line)

Сведения об образовательной организации

UDK 519.632
APPLICATION OF HERMITIAN BIQUADRATIC FINITE ELEMENT
V. V. Shaydurov [1, 3], S. V. Shut [ 2]
[1] Siberian State Aerospace University named after academician M. F. Reshetnev 31, Krasnoyarsky Rabochy Av., Krasnoyarsk, 660014, Russian Federation [2] Siberian Federal University 79, Svobodny prosp., Krasnoyarsk, 660041, Russian Federation E-mail: seshoot@mail.ru [3] Institute of Computational Modeling of Siberian Branch of Russian Academy of Science 50/44, Akademgorodok, Krasnoyarsk, 660036, Russian Federation E-mail: shaidurov04@mail.ru
A new type of Hermitian finite element on rectangle is presented which is intermediate between bilinear and bicubic finite elements. The use of this biquadratic element gives less number of unknowns and equations of discrete algebraic systems in comparison with the Lagrangian element of the same degree. The theoretical conclusion of its effectiveness is illustrated by using this finite element for solving boundary value problem for second-order elliptic equation where the second order of accuracy was achieved for approximate solution in the energy norm and the fourth order of accu-racy in mean-value norm on uniform mesh.
finite element method, Hermitian and Lagrangian finite elements, number of degrees of freedom, order of approximation, order of convergence.
References

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7. Gileva L., Shaydurov V., Dobronets B. The triangu-lar Hermite finite element complementing the Bogner-Fox-Schmit rectangle. Applied Mathematics. 2013. Vol. 5, no. 12A, p. 50–56.

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9. Zhang S. On the full C1-Qk finite element spaces on rectangles and cuboids. Advances in Applied Mathematics and Mechanics. 2010. Vol. 2, no. 6, p. 701–721.

10. Adams R. A., Fournier J. J. F. Sobolev spaces. New York, Academic Press, 2003.


Shaidurov Vladimir Viktorovich – Corresponding member of Russian Academy of Sciences, Doctor of Sciences (physics and mathematics), Professor, Director of Institute of Computational Modeling of Siberian Branch of Russian Academy of Sciences; Director of Institute of Space Research and High Technologies of Siberian State Aerospace Uni-versity named after academician M. F. Reshetnev. Е-mail: shaidurov04@mail.ru.

Shut Sergey Vladimirovich – postgraduate student, Siberian Federal University. E-mail: seshoot@mail.ru