Versions of the collocation and least squares method for solving biharmonic equations in non-canonical domains

Результат исследования: Публикации в книгах, отчётах, сборниках, трудах конференцийстатья в сборнике материалов конференциинаучнаярецензирование

2 Цитирования (Scopus)

Аннотация

New versions of the collocations and least squares method of high-order accuracy are proposed and implemented for the numerical solution of the boundary value problems for the biharmonic equation in non-canonical domains. The solution of the biharmonic equation is used for simulating the stress-strain state of an isotropic plate under the action of transverse load. The differential problem is projected into a space of fourth-degree polynomials by the CLS method. The boundary conditions for the approximate solution are put down exactly on the boundary of the computational domain. The versions of the CLS method are implemented on the grids which are constructed in two different ways. It is shown that the approximate solution of problems converges with high order. Thus it matches with high accuracy with the analytical solution of the test problems in the case of known solution in the numerical experiments on the convergence of the solution of various problems on a sequence of grids.

Язык оригиналаанглийский
Название основной публикацииProceedings of the XXV Conference on High-Energy Processes in Condensed Matter, HEPCM 2017
Подзаголовок основной публикацииDedicated to the 60th Anniversary of the Khristianovich Institute of Theoretical and Applied Mechanics SB RAS
Редакторы Fomin
ИздательAmerican Institute of Physics Inc.
Число страниц14
Том1893
ISBN (электронное издание)9780735415782
DOI
СостояниеОпубликовано - 26 окт 2017
Событие25th Conference on High-Energy Processes in Condensed Matter, HEPCM 2017 - Novosibirsk, Российская Федерация
Продолжительность: 5 июн 20179 июн 2017

Серия публикаций

НазваниеAIP Conference Proceedings
ИздательAMER INST PHYSICS
Том1893
ISSN (печатное издание)0094-243X

Конференция

Конференция25th Conference on High-Energy Processes in Condensed Matter, HEPCM 2017
СтранаРоссийская Федерация
ГородNovosibirsk
Период05.06.201709.06.2017

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  • Цитировать

    Belyaev, V. A., & Shapeev, V. P. (2017). Versions of the collocation and least squares method for solving biharmonic equations in non-canonical domains. В Fomin (Ред.), Proceedings of the XXV Conference on High-Energy Processes in Condensed Matter, HEPCM 2017: Dedicated to the 60th Anniversary of the Khristianovich Institute of Theoretical and Applied Mechanics SB RAS (Том 1893). [030102] (AIP Conference Proceedings; Том 1893). American Institute of Physics Inc.. https://doi.org/10.1063/1.5007560