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 -