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

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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. / Belyaev, V. A.; Bryndin, L. S.; Golushko, S. K. et al.

In: Computational Mathematics and Mathematical Physics, Vol. 62, No. 4, 04.2022, p. 517-537.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{6f19396375054e6d972bbe3bf3318616,

title = "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",

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.",

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

author = "Belyaev, {V. A.} and Bryndin, {L. S.} and Golushko, {S. K.} and Semisalov, {B. V.} and Shapeev, {V. P.}",

note = "Funding Information: This work was performed in the framework of the state assignment (state registration nos. 121030500137-5 and AAAA-A19-119051590004-5) and was supported in part by the Russian Foundation for Basic Research (project no. 18-29-18029). Publisher Copyright: {\textcopyright} 2022, Pleiades Publishing, Ltd.",

year = "2022",

month = apr,

doi = "10.1134/S0965542522040029",

language = "English",

volume = "62",

pages = "517--537",

journal = "Computational Mathematics and Mathematical Physics",

issn = "0965-5425",

publisher = "PLEIADES PUBLISHING INC",

number = "4",

}

RIS

TY - JOUR

T1 - 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

AU - Belyaev, V. A.

AU - Bryndin, L. S.

AU - Golushko, S. K.

AU - Semisalov, B. V.

AU - Shapeev, V. P.

N1 - Funding Information: This work was performed in the framework of the state assignment (state registration nos. 121030500137-5 and AAAA-A19-119051590004-5) and was supported in part by the Russian Foundation for Basic Research (project no. 18-29-18029). Publisher Copyright: © 2022, Pleiades Publishing, Ltd.

PY - 2022/4

Y1 - 2022/4

N2 - 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.

AB - 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.

KW - bending of isotropic plate

KW - biharmonic equation

KW - boundary value problem

KW - higher order of convergence

KW - irregular multiply-connected domain

KW - least-squares collocation method

UR - http://www.scopus.com/inward/record.url?scp=85130838797&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/6eaeacf9-c71c-360a-af5b-c22618340cff/

U2 - 10.1134/S0965542522040029

DO - 10.1134/S0965542522040029

M3 - Article

AN - SCOPUS:85130838797

VL - 62

SP - 517

EP - 537

JO - Computational Mathematics and Mathematical Physics

JF - Computational Mathematics and Mathematical Physics

SN - 0965-5425

IS - 4

ER -

ID: 36187911