Error estimates of vibrations of elastic string with moving ends

Authors:
M. A. Rincon;I.-Shih Liu
Affiliations:
Instituto de Matemática, Universidade Federal do Rio de Janeiro, Rio de Janeiro, Brazil;Instituto de Matemática, Universidade Federal do Rio de Janeiro, Rio de Janeiro, Brazil
Venue:
Applied Numerical Mathematics
Year:
2006

Citing 2
Cited 0

Finite Element Method for Elliptic Problems

Finite Element Method for Elliptic Problems
Effect of moving boundaries on the vibrating elastic string

Applied Numerical Mathematics - Special issue: 2nd international workshop on numerical linear algebra, numerical methods for partial differential equations and optimization

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Abstract

In this work, a mathematical model for small vibrations of an elastic string with moving boundaries is discussed. Global existence and uniqueness of solutions have been established in [M.A. Rincon, I.-S. Liu, Existence and uniqueness of solutions of elastic string with moving ends, Math. Methods Appl. Sci. 27 (14) (2004) 1641-1655]. The objective of this paper is to obtain the error estimates of solutions in Sobolev spaces for the semi-discrete problem, with discretization of space variable and continuous time. The analysis is based on Galerkin finite element method.