Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Research › peer-review
Versions of the collocation and least squares method for solving biharmonic equations in non-canonical domains. / Belyaev, V. A.; Shapeev, V. P.
Proceedings of the XXV Conference on High-Energy Processes in Condensed Matter, HEPCM 2017: Dedicated to the 60th Anniversary of the Khristianovich Institute of Theoretical and Applied Mechanics SB RAS. ed. / Fomin. Vol. 1893 American Institute of Physics Inc., 2017. 030102 (AIP Conference Proceedings; Vol. 1893).Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Research › peer-review
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TY - GEN
T1 - Versions of the collocation and least squares method for solving biharmonic equations in non-canonical domains
AU - Belyaev, V. A.
AU - Shapeev, V. P.
PY - 2017/10/26
Y1 - 2017/10/26
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85034262260&partnerID=8YFLogxK
U2 - 10.1063/1.5007560
DO - 10.1063/1.5007560
M3 - Conference contribution
AN - SCOPUS:85034262260
VL - 1893
T3 - AIP Conference Proceedings
BT - Proceedings of the XXV Conference on High-Energy Processes in Condensed Matter, HEPCM 2017
A2 - Fomin, null
PB - American Institute of Physics Inc.
T2 - 25th Conference on High-Energy Processes in Condensed Matter, HEPCM 2017
Y2 - 5 June 2017 through 9 June 2017
ER -
ID: 9696262