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Robust 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:  09 January 2017

Xiaojing Xu and
Xiaoping Xie
Xiaojing Xu
Affiliation:
School of Science, Southwest University of Science and Technology, Mianyang, Sichuan 621010, China
Xiaoping Xie*
Affiliation:
School of Mathematics, Sichuan University, Chengdu, Sichaun 610064, China
*
*Corresponding author. Email:xuxiaojing0603@126.com (X. J. Xu), xpxie@scu.edu.cn (X. P. Xie)

Abstract

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This paper analyzes semi-discrete and fully discrete hybrid stress quadrilateral finite element methods for 2-dimensional linear elastodynamic problems. The methods use a 4 node hybrid stress quadrilateral element in the space discretization. In the fully discrete scheme, an implicit second-order scheme is adopted in the time discretization. We derive optimal a priori error estimates for the two schemes and an unconditional stability result for the fully discrete scheme. Numerical experiments confirm the theoretical results.

Keywords

Elastodynamic problemhybrid stress finite elementsemi-discretefully discreteerror estimate

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
Advances in Applied Mathematics and Mechanics , Volume 9 , Issue 2 , April 2017, pp. 324 - 348
Copyright
Copyright © Global-Science Press 2017 

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