The least squares collocation method for the biharmonic equation in irregular and multiply-connected domains

Vasily Shapeev; Sergey Golushko; Luka Bryndin; Vasily Belyaev

doi:10.1088/1742-6596/1268/1/012076

The least squares collocation method for the biharmonic equation in irregular and multiply-connected domains

Vasily Shapeev, Sergey Golushko, Luka Bryndin, Vasily Belyaev

Результат исследования: Научные публикации в периодических изданиях › статья по материалам конференции › рецензирование

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Аннотация

This paper reports new h-and p-versions of the least squares collocation method of high-order accuracy proposed and implemented for solving boundary value problems for the biharmonic equation in irregular and multiply-connected domains. This paper shows that approximate solutions obtained by the least squares collocation method converge with high order and agree with analytical solutions of test problems with high degree of accuracy. There has been a comparison made for the results achieved in this study and results of other authors who used finite difference and spectral methods.

Язык оригинала	английский
Номер статьи	012076
Число страниц	7
Журнал	Journal of Physics: Conference Series
Том	1268
Номер выпуска	1
DOI	https://doi.org/10.1088/1742-6596/1268/1/012076
Состояние	Опубликовано - 16 июл 2019
Событие	All-Russian Conference and School for Young Scientists, devoted to 100th Anniversary of Academician L.V. Ovsiannikov on Mathematical Problems of Continuum Mechanics, MPCM 2019 - Novosibirsk, Российская Федерация Продолжительность: 13 мая 2019 → 17 мая 2019

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10.1088/1742-6596/1268/1/012076

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The least squares collocation method for the biharmonic equation in irregular and multiply-connected domains. / Shapeev, Vasily ; Golushko, Sergey ; Bryndin, Luka; Belyaev, Vasily.

В: Journal of Physics: Conference Series, Том 1268, № 1, 012076, 16.07.2019.

Результат исследования: Научные публикации в периодических изданиях › статья по материалам конференции › рецензирование

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AB - This paper reports new h-and p-versions of the least squares collocation method of high-order accuracy proposed and implemented for solving boundary value problems for the biharmonic equation in irregular and multiply-connected domains. This paper shows that approximate solutions obtained by the least squares collocation method converge with high order and agree with analytical solutions of test problems with high degree of accuracy. There has been a comparison made for the results achieved in this study and results of other authors who used finite difference and spectral methods.

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