h-, p-, and hp-Versions of the Least-Squares Collocation Method for Solving Boundary Value Problems for Biharmonic Equation in Irregular Domains and Their Applications

h-, p-, and hp-Versions of the Least-Squares Collocation Method for Solving Boundary Value Problems for Biharmonic Equation in Irregular Domains and Their Applications Full article

Journal

Computational Mathematics and Mathematical Physics
ISSN: 0965-5425 , E-ISSN: 1555-6662

Output data

Year: 2022, Volume: 62, Number: 4, Pages: 517-537 Pages count : 21 DOI: 10.1134/S0965542522040029

Tags

bending of isotropic plate; biharmonic equation; boundary value problem; higher order of convergence; irregular multiply-connected domain; least-squares collocation method

Authors

Belyaev V.A. ^1,2 , Bryndin L.S. ^1,2 , Golushko S.K. ^2,3 , Semisalov B.V. ^2,4 , Shapeev V.P. ^1,2

Affiliations

1	Khristianovich Institute of Theoretical and Applied Mechanics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russian Federation
2	Novosibirsk State University, Novosibirsk, 630090, Russian Federation
3	Federal Research Center for Information and Computational Technologies, Novosibirsk, 630090, Russian Federation
4	Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russian Federation

Funding (2)

1	Khristianovich Institute of Theoretical and Applied Mechanics, Novosibirsk, Russia	121030500137-5
2	Russian Foundation for Basic Research	18-29-18029

Abstract: New h-, p-, and hp-versions of the least-squares collocation method are proposed and implemented. They yield approximate solutions of boundary value problems for an inhomogeneous biharmonic equation in irregular and multiply-connected domains. Formulas for the extension operation in the transition from coarse to finer grids on a multigrid complex are given in the case of applying various spaces of polynomials. It is experimentally shown that numerical solutions of boundary value problems produced by the developed versions of the method have a higher order of convergence to analytical solutions with no singularities. The results are compared with those of other authors produced by applying finite difference, finite element, and other methods based on Chebyshev polynomials. Examples of problems with singularities are considered. The developed versions of the method are used to simulate the bending of an elastic isotropic plate of irregular shape subjected to transverse loading.

Belyaev V.A. , Bryndin L.S. , Golushko S.K. , Semisalov B.V. , Shapeev V.P.
h-, p-, and hp-Versions of the Least-Squares Collocation Method for Solving Boundary Value Problems for Biharmonic Equation in Irregular Domains and Their Applications
Computational Mathematics and Mathematical Physics. 2022. V.62. N4. P.517-537. DOI: 10.1134/S0965542522040029 WOS Scopus РИНЦ OpenAlex

Беляев В.А. , Брындин В.Д. , Голушко С.К. , Semisalov B.V. , Шапеев В.П.
H-, P- и HР-варианты метода коллокации и наименьших квадратов для решения краевых задач для бигармонического уравнения в нерегулярных областях и их приложения
Журнал вычислительной математики и математической физики. 2022. V.62. N4. P.531–552. DOI: 10.31857/S0044466922040020 РИНЦ

Submitted:	Feb 10, 2020
Accepted:	Nov 16, 2021
Published online:	May 27, 2022

Web of science:	WOS:000800838600001
Scopus:	2-s2.0-85130838797
Elibrary:	48586497
OpenAlex:	W4281709696

DB	Citing
Scopus	8
Web of science	7
OpenAlex	9
Elibrary	5