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Volume 9, Issue 2
Robust Semi-Discrete and Fully Discrete Hybrid Stress Finite Element Methods for Elastodynamic Problems

Xiaojing Xu & Xiaoping Xie

DOI: 10.4208/aamm.2015.m1326

Adv. Appl. Math. Mech., 9 (2017), pp. 324-348.

Published online: 2018-05

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  • Abstract

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 problem, hybrid stress finite element, semi-discrete, fully discrete, error estimate.

  • AMS Subject Headings

65N12, 65N15, 65N30

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-9-324, author = {Xu , Xiaojing and Xie , Xiaoping}, title = {Robust Semi-Discrete and Fully Discrete Hybrid Stress Finite Element Methods for Elastodynamic Problems}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2018}, volume = {9}, number = {2}, pages = {324--348}, abstract = {

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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.2015.m1326}, url = {http://global-sci.org/intro/article_detail/aamm/12151.html} }
TY - JOUR T1 - Robust Semi-Discrete and Fully Discrete Hybrid Stress Finite Element Methods for Elastodynamic Problems AU - Xu , Xiaojing AU - Xie , Xiaoping JO - Advances in Applied Mathematics and Mechanics VL - 2 SP - 324 EP - 348 PY - 2018 DA - 2018/05 SN - 9 DO - http://doi.org/10.4208/aamm.2015.m1326 UR - https://global-sci.org/intro/article_detail/aamm/12151.html KW - Elastodynamic problem, hybrid stress finite element, semi-discrete, fully discrete, error estimate. AB -

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.

Xu , Xiaojing and Xie , Xiaoping. (2018). Robust Semi-Discrete and Fully Discrete Hybrid Stress Finite Element Methods for Elastodynamic Problems. Advances in Applied Mathematics and Mechanics. 9 (2). 324-348. doi:10.4208/aamm.2015.m1326
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