Versions of the collocation and least squares method for solving biharmonic equations in non-canonical domains

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Abstract

New versions of the collocations and least squares method of high-order accuracy are proposed and implemented for the numerical solution of the boundary value problems for the biharmonic equation in non-canonical domains. The solution of the biharmonic equation is used for simulating the stress-strain state of an isotropic plate under the action of transverse load. The differential problem is projected into a space of fourth-degree polynomials by the CLS method. The boundary conditions for the approximate solution are put down exactly on the boundary of the computational domain. The versions of the CLS method are implemented on the grids which are constructed in two different ways. It is shown that the approximate solution of problems converges with high order. Thus it matches with high accuracy with the analytical solution of the test problems in the case of known solution in the numerical experiments on the convergence of the solution of various problems on a sequence of grids.

Original languageEnglish
Title of host publicationProceedings of the XXV Conference on High-Energy Processes in Condensed Matter, HEPCM 2017
Subtitle of host publicationDedicated to the 60th Anniversary of the Khristianovich Institute of Theoretical and Applied Mechanics SB RAS
Editors Fomin
PublisherAmerican Institute of Physics Inc.
Number of pages14
Volume1893
ISBN (Electronic)9780735415782
DOIs
Publication statusPublished - 26 Oct 2017
Event25th Conference on High-Energy Processes in Condensed Matter, HEPCM 2017 - Novosibirsk, Russian Federation
Duration: 5 Jun 20179 Jun 2017

Publication series

NameAIP Conference Proceedings
PublisherAMER INST PHYSICS
Volume1893
ISSN (Print)0094-243X

Conference

Conference25th Conference on High-Energy Processes in Condensed Matter, HEPCM 2017
CountryRussian Federation
CityNovosibirsk
Period05.06.201709.06.2017

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