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Semi-Discrete and Fully Discrete Hybrid Stress Finite Element Methods for Elastodynamic Problems

Part of:Partial differential equations, boundary value problems

Published online by Cambridge University Press:  10 November 2015

Zhengqin Yu and
Xiaoping Xie
Zhengqin Yu
Affiliation:
School of Mathematics, Sichuan University, Chengdu 610064, China
Xiaoping Xie*
Affiliation:
School of Mathematics, Sichuan University, Chengdu 610064, China
*
*Corresponding author. Email addresses: zhengqinyulm@sina.com (Z. Yu), xpxie@scu.edu.cn (X. Xie)

Abstract

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This paper proposes and analyzes semi-discrete and fully discrete hybrid stress finite element methods for elastodynamic problems. A hybrid stress quadrilateral finite element approximation is used in the space directions. A second-order center difference is adopted in the time direction for the fully discrete scheme. Error estimates of the two schemes, as well as a stability result for the fully discrete scheme, are derived. Numerical experiments are done to verify the theoretical results.

Keywords

elastodynamic problemhybrid stress finite elementsemi-discretefully discrete

MSC classification

Secondary:65N12: Stability and convergence of numerical methods65N15: Error bounds65N30: Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods

Information

Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 8 , Issue 4 , November 2015, pp. 582 - 604
Copyright
Copyright © Global-Science Press 2015 

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