| Инд. авторы: | Shapeev V., Golushko S., Bryndin L., Belyaev V. |
| Заглавие: | The least squares collocation method for the biharmonic equation in irregular and multiply-connected domains |
| Библ. ссылка: | Shapeev V., Golushko S., Bryndin L., Belyaev V. The least squares collocation method for the biharmonic equation in irregular and multiply-connected domains // Journal of Physics: Conference Series. - 2019. - Vol.1268. - Iss. 1. - Art.012076. - ISSN 1742-6588. - EISSN 1742-6596. |
| Внешние системы: | DOI: 10.1088/1742-6596/1268/1/012076; РИНЦ: 41555501; SCOPUS: 2-s2.0-85073915160; WoS: 000561766800076; |
| Реферат: | eng: 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. © Published under licence by IOP Publishing Ltd. |
| Ключевые слова: | Spectral methods; Multiply connected domain; Least-squares collocation; High-order accuracy; High degree of accuracy; Biharmonic equations; Approximate solution; Continuum mechanics; Boundary value problems; H and p-version; Least squares approximations; |
| Издано: | 2019 |
| Физ. характеристика: | 012076 |
| Конференция: | Название: Всероссийская конференция и школа для молодых ученых, посвященные 100-летию академика Л.В. Овсянникова, «Математические проблемы механики сплошных сред» Аббревиатура: MPCM 2019 Город: Новосибирск Страна: Россия Даты проведения: 2019-05-13 - 2019-05-17 |
| Цитирование: | 1. Timoshenko S P and Woinowsky-Krieger S 1959 Theory of Plates and Shells 2 (New York: McGraw-Hill Book Company) 580 2. Chen G, Li Z and Lin P. 2007. // Adv. Comput. Math. 29 113-33 3. Ben-Artzi M, Chorev I, Croisille J P and Fishelov D 2009 SIAM J. Numer. Anal. 47 3087-108 4. Brenner S C 1989 SIAM J. Numer. Anal. 26 1124-38 5. Mayo A and Greenbaum A 1992 SIAM J. Sci. Comput. 13 101-18 6. Hanisch M R 1993 SIAM J. Numer. Anal. 30 184-214 7. Davini C and Pitacco I 2000 SIAM J. Numer. Anal. 38 820-36 8. Eymard R, Gallouët T, Herbin R and Linke A. 2012 // Math. Comp. 812 2019-48 9. Shao W, Wu X and Chen S. 2012 // Engin. Anal. Bound. Elem. 36 1787-98 10. Mai-Duy N, See H and Tran-Cong T. 2009 // Appl. Math. Model. 33 284-99 11. Shao W and Wu X. 2015 // Appl. Math. Model. 39 2554-69 12. Zhuang Q and Chen L. 2017 // Comp. Math. Appl. 75 2958-68 13. Jiang Y, Wang B and Yuesheng X 2014 SIAM J. Numer. Anal. 52 2530-54 14. Shapeev V P, Belyaev V A, Golushko S K and Idimeshev S V 2017 EPJ Web of Conf. 173 01012-1 15. Shapeev V P and Belyaev V A 2018 Numer. Methods Program. 19 340-55 in Russian 16. Saad Y 1992 Numerical Methods for Large Eigenvalue Problems (Manchester: Manchester University Press) 346 17. Fedorenko R P 1964 USSR Comput. Math. Math. Phys. 4 559-64 18. Ramšak M and Skerget L A 2004 Int. J. Numer. Meth. Fluids. 46 815-47 19. Golushko S K, Idimeshev S V and Shapeev V P 2014 Computat. Technolog. 19 24-36 in Russian 20. Belyaev V A and Shapeev V P 2018 Computat. Technolog. 23 15-30 in Russian |
