Estimation of the error of the Galerkin method in the study of the dynamics of an elastic plate

Title	Estimation of the error of the Galerkin method in the study of the dynamics of an elastic plate
Authors	M. A. Ankilov¹, A. S. Andreev¹ ¹Ulyanovsk State University
Annotation	In this paper, based on the simplest mathematical model of free vibrations of an elastic plate, an analytical method for studying its dynamics is developed. The case of hinged fastening of the ends of the elastic plate is investigated. The model is described by a differential equation in partial derivatives, the solution of which is found by the Bubnov-Galerkin method. The purpose of the study is to determine the error of the obtained approximate solution based on the construction of a Lyapunov-type functional.
Keywords	mathematical modeling, dynamics, elastic plate, Galerkin method.
Citation	Ankilov M. A., Andreev A. S. ''Estimation of the error of the Galerkin method in the study of the dynamics of an elastic plate'' [Electronic resource]. Proceedings of the International Scientific Youth School-Seminar "Mathematical Modeling, Numerical Methods and Software complexes" named after E.V. Voskresensky (Saransk, July 29-31, 2025). Saransk: SVMO Publ, 2025. - pp. 45-49. Available at: https://conf.svmo.ru/files/2025/papers/paper07.pdf. - Date of access: 30.08.2025.