Труды сотрудников ИВМ СО РАН

[Text] / L. V. Gileva, V. V. Shaidurov // Russ. J. Numer. Anal. Math. Model. - 2009. - Vol. 24, Is. 5. - P425-438, DOI 10.1515/RJNAMM.2009.027. - Cited References: 11. - This analysis was partially supported by Grant 08-01-00621 of the Russian Foundation of Basic Research. . - ISSN 0927-6467РУБ Engineering, Multidisciplinary + Mathematics, Applied

Аннотация: In this paper, a full multigrid algorithm with a symmetric V-cycle for a grid problem obtained by discretization of a second-order elliptic equation with quadratic finite elements on triangles is studied. The multigrid complexity of the algorithm is proved. This means that the number of arithmetic operations required to achieve the order of accuracy of an approximate solution equal to that of the discretization error linearly depends on the number of unknowns. The rate of convergence is found to be higher than that for linear finite elements in spite of the higher order of accuracy.


Доп.точки доступа:
Shaidurov, V.V.; Шайдуров, Владимир Викторович; Гилева, Лидия Викторовна; Russian Foundation [08-01-00621]

[Text] : статья / L. Gileva, V. Shaydurov, B. Dobronets // Applied Mathematics. - 2013. - Vol. 4. - p. 50-56DOI 10.4236/am.2013.412A006 . -
Аннотация: The Bogner-Fox-Schmit rectangular element is one of the simplest elements that provide continuous differentiability of an approximate solution in the framework of the finite element method. However, it can be applied only on a simple domain composed of rectangles or parallelograms whose sides are parallel to two different straight lines. We propose a new triangular Hermite element with 13 degrees of freedom. It is used in combination with the Bogner-Fox-Schmit element near the boundary of an arbitrary polygonal domain and provides continuous differentiability of an approximate solution in the whole domain up to the boundary.

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Доп.точки доступа:
Shaydurov, V.V.; Шайдуров, Владимир Викторович; Dobronets, B.S.; Добронец, Борис Станиславович; Гилева, Лидия Викторовна

[Text] / L. Gileva, V. Shaidurov, B. Dobronets // Russ. J. Numer. Anal. Math. Model. - 2015. - Vol. 30, Is. 2. - P73-85, DOI 10.1515/rnam-2015-0008. - Cited References:23. - The work was supported by the Russian Scientific Foundation (Project 14-11-00147). . - ISSN 0927-6467. - ISSN 1569-3988РУБ Engineering, Multidisciplinary + Mathematics, Applied

Аннотация: The Bogner-Fox-Schmit rectangular element is one of the simplest elements that provide continuous differentiability of an approximate solution in the framework of the finite element method. However, it can be applied only on a simple domain composed of rectangles whose sides are parallel to two different straight lines. We propose a new family of triangular Hermite elements that involves straight-sided elements and elements with a curved side. Such an element can be used in combination with the Bogner-Fox-Schmit element near the boundary of an arbitrary polygonal domain or a domain with a curved part of the boundary and provides continuous differentiability of an approximate solution in the whole domain up to the boundary.

WOS,
Scopus

Держатели документа:
RAS, Siberian Branch, Inst Computat Modelling, Krasnoyarsk 660036, Russia.
Beihang Univ, Beijing 100191, Peoples R China.
Siberian Fed Univ, Krasnoyarsk 660049, Russia.

Доп.точки доступа:
Gileva, L.V.; Гилева, Лидия Викторовна; Shaidurov, V.V.; Шайдуров, Владимир Викторович; Dobronets, B.S.; Добронец, Борис Станиславович; Russian Scientific Foundation [14-11-00147]

[Текст] : научное издание / Л. В. Гилева, Е. Д. Карепова, В. В. Шайдуров // Решетневские чтения. - 2016. - Т. 2, № 20. - С. 126-127 . - ISSN 1990-7702
   Перевод заглавия: A FAMILY OF BICUBIC HERMITE FINITE ELEMENT ON RECTANGLES AND TRIANGLES

УДК

519.63

Аннотация: Предложен новый бикубический эрмитов элемент на прямоугольнике и дополняющие его треугольные эрмитовы элементы, в том числе на треугольнике с криволинейной стороной. Совместное использование прямоугольных и треугольных элементов позволяет применять их для решения задач в многоугольных облостях и областях с криволинейными участками границы.
In the paper, a new bicubic Hermite element on a rectangle and related Hermite elements on a straight-sided triangle and on a triangle with a curved side are proposed. The combination of these elements enables one to apply them for problems in a polygonal domain and in a domain with curved parts of the boundary.

РИНЦ

Держатели документа:
Институт вычислительного моделирования СО РАН

Доп.точки доступа:
Гилева, Л.В.; Gileva L.V.; Карепова, Е.Д.; Karepova E.D.; Шайдуров, В.В.; Shaidurov V.V.

[Текст] : статья / Л. В. Гилева, Е. Д. Карепова, А. А. Пьяных // Решетневские чтения. - 2018. - Т. 1, № 22. - С. 564-565 . - ISSN 1990-7702
   Перевод заглавия: The application of special Hermite finite elements to the diffusion equation with a variable coefficient

УДК

519.632.4

Аннотация: Для уравнения диффузии с переменным коэффициентом предложен численный метод, основанный на использовании специальных бикубических эрмитовых элементов в сочетании с методом коллокации. Результаты расчетов показали высокую эффективность метода.
For the diffusion equation with a variable coefficient, a numerical method based on the use of special bicubic Hermite elements coupled with collocation is proposed. As a result, the dimension of the system of equations is reduced in comparison with the standard finite element scheme with the order of convergence of an approximate solution remaining unchanged. In the two-dimensional case, a convergence estimate is proved and confirmed with numerical experiments. Besides, for the one-dimensional case, numerical experiments with the standard Lagrange and Hermite cubic elements as well as with the special Hermite cubic elements proposed by the authors are performed. Numerical results demonstrate high efficiency of the last ones.

РИНЦ

Держатели документа:
Институт вычислительного моделирования СО РАН

Доп.точки доступа:
Гилева, Л.В.; Gileva L.V.; Карепова, Е.Д.; Karepova E.D.; Пьяных, А.А.; Pianykh A.A.