Convergence analysis of the spectral element method on the example of the Lamb problem in comparison with the analytical solution
https://doi.org/10.22405/2226-8383-2026-27-1-153-165
Abstract
The convergence analysis of the spectral element method (one of the modern modifications of the finite element method) for the dynamic problem of elasticity theory is performed by comparing the numerical solution with the analytical solution of the Lamb problem — the
problem of dynamic action on the boundary of a half-plane or half-space by a concentrated or distributed load changing according to some time law. The article considers the effect on the boundary of a load changing according to the Berlage time law. The calculations are
performed using the domestic strength software package “Fidesys”. Stress distribution graphs for the material under study are given. The dependence of the error of the numerical solution on the order of elements for a fixed number of points per Rayleigh wavelength is investigated.
About the Authors
Vladimir Anatol’evich Levin
Lomonosov Moscow State University
Russian Federation
Russian Federation
doctor of physical and mathematical sciences, professor
Anatoliy Victorovich Vershinin
Lomonosov Moscow State University
Russian Federation
Russian Federation
doctor of physical and mathematical sciences
Konstantin Moiseevich Zingerman
Tver State University
Russian Federation
Russian Federation
doctor of physical and mathematical sciences, professor
Evgeny Mikhailovich Ukhanov
Lomonosov Moscow State University
Russian Federation
Russian Federation
student
References
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Review
For citations:
Levin V.A., Vershinin A.V., Zingerman K.M., Ukhanov E.M. Convergence analysis of the spectral element method on the example of the Lamb problem in comparison with the analytical solution. Chebyshevskii Sbornik. 2026;27(1):153-165. (In Russ.) https://doi.org/10.22405/2226-8383-2026-27-1-153-165
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