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

被引：2

作者：

Shapeev, Vasily ^{[1
,2
]}

Golushko, Sergey ^{[1
,3
]}

Bryndin, Luka ^{[1
,2
]}

Belyaev, Vasily ^{[2
]}

机构：

[1] Novosibirsk State Univ, Novosibirsk, Russia

[2] Khristianovich Inst Theoret & Appl Mech SB RAS, Novosibirsk, Russia

[3] Inst Computat Technol SB RAS, Novosibirsk, Russia

来源：

ALL-RUSSIAN CONFERENCE AND SCHOOL FOR YOUNG SCIENTISTS, DEVOTED TO 100TH ANNIVERSARY OF ACADEMICIAN L.V. OVSIANNIKOV - MATHEMATICAL PROBLEMS OF CONTINUUM MECHANICS | 2019年 / 1268卷

基金：

俄罗斯基础研究基金会;

关键词：

ELEMENT METHOD;

D O I：

10.1088/1742-6596/1268/1/012076

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页数：7

共 50 条

[1] Solving the Biharmonic Equation in Irregular Domains by the Least Squares Collocation Method
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[J]. INTERNATIONAL CONFERENCE ON THE METHODS OF AEROPHYSICAL RESEARCH (ICMAR 2018), 2018, 2027
[2] A h-Version of the Least Squares Collocation Method for the Biharmonic Equation in Irregular Domains
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Bryndin, Luka
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[J]. VII INTERNATIONAL CONFERENCE ON CURRENT ISSUES OF CONTINUUM MECHANICS AND CELESTIAL MECHANICS, 2019, 1214
[3] A transform method for the biharmonic equation in multiply connected circular domains
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[J]. IMA JOURNAL OF APPLIED MATHEMATICS, 2018, 83 (06) : 942 - 976
[4] A transform method for the biharmonic equation in multiply connected circular domains
[J]. Luca, Elena (elouca@ucsd.edu), 1600, Oxford University Press (83):
[5] The hp-version of the least-squares collocation method with integral collocation for solving a biharmonic equation
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[J]. VESTNIK SAMARSKOGO GOSUDARSTVENNOGO TEKHNICHESKOGO UNIVERSITETA-SERIYA-FIZIKO-MATEMATICHESKIYE NAUKI, 2022, 26 (03): : 556 - 572
[6] Versions of the Collocation and Least Squares Method for Solving Biharmonic Equations in Non-canonical Domains
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[J]. PROCEEDINGS OF THE XXV CONFERENCE ON HIGH-ENERGY PROCESSES IN CONDENSED MATTER (HEPCM 2017), 2017, 1893
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[J]. AMERICAN JOURNAL OF MATHEMATICS, 1946, 68 (01) : 20 - 28
[8] ON CONFORMAL MAPPING OF MULTIPLY-CONNECTED DOMAINS
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[9] THE COEFFICIENT PROBLEM FOR MULTIPLY-CONNECTED DOMAINS
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