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Volume 12, Issue 4
A Locking-Free DP-Q2-P1 MFEM for Incompressible Nonlinear Elasticity Problems

Weijie Huang & Zhiping Li

DOI: 10.4208/nmtma.OA-2018-0087

Numer. Math. Theor. Meth. Appl., 12 (2019), pp. 995-1011.

Published online: 2019-06

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  • Abstract

A mixed finite element method (MFEM), using dual-parametric piecewise biquadratic and affine (DP-Q2-P1) finite element approximations for the deformation and the pressure like Lagrange multiplier respectively, is developed and analyzed for the numerical computation of incompressible nonlinear elasticity problems with large deformation gradient, and a damped Newton method is applied to solve the resulted discrete problem. The method is proved to be locking free and stable. The accuracy and efficiency of the method are illustrated by numerical experiments on some typical cavitation problems.

  • Keywords

DP-Q2-P1 mixed finite element, damped Newton method, locking-free, incompressible nonlinear elasticity, large deformation gradient, cavitation.

  • AMS Subject Headings

65N12, 65N30, 74B20, 74G15, 74M99

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

huangwj@pku.edu.cn (Weijie Huang)

lizp@math.pku.edu.cn (Zhiping Li)

  • BibTex
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  • TXT
@Article{NMTMA-12-995, author = {Huang , Weijie and Li , Zhiping}, title = {A Locking-Free DP-Q2-P1 MFEM for Incompressible Nonlinear Elasticity Problems}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2019}, volume = {12}, number = {4}, pages = {995--1011}, abstract = {

A mixed finite element method (MFEM), using dual-parametric piecewise biquadratic and affine (DP-Q2-P1) finite element approximations for the deformation and the pressure like Lagrange multiplier respectively, is developed and analyzed for the numerical computation of incompressible nonlinear elasticity problems with large deformation gradient, and a damped Newton method is applied to solve the resulted discrete problem. The method is proved to be locking free and stable. The accuracy and efficiency of the method are illustrated by numerical experiments on some typical cavitation problems.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.OA-2018-0087}, url = {http://global-sci.org/intro/article_detail/nmtma/13210.html} }
TY - JOUR T1 - A Locking-Free DP-Q2-P1 MFEM for Incompressible Nonlinear Elasticity Problems AU - Huang , Weijie AU - Li , Zhiping JO - Numerical Mathematics: Theory, Methods and Applications VL - 4 SP - 995 EP - 1011 PY - 2019 DA - 2019/06 SN - 12 DO - http://doi.org/10.4208/nmtma.OA-2018-0087 UR - https://global-sci.org/intro/article_detail/nmtma/13210.html KW - DP-Q2-P1 mixed finite element, damped Newton method, locking-free, incompressible nonlinear elasticity, large deformation gradient, cavitation. AB -

A mixed finite element method (MFEM), using dual-parametric piecewise biquadratic and affine (DP-Q2-P1) finite element approximations for the deformation and the pressure like Lagrange multiplier respectively, is developed and analyzed for the numerical computation of incompressible nonlinear elasticity problems with large deformation gradient, and a damped Newton method is applied to solve the resulted discrete problem. The method is proved to be locking free and stable. The accuracy and efficiency of the method are illustrated by numerical experiments on some typical cavitation problems.

Huang , Weijie and Li , Zhiping. (2019). A Locking-Free DP-Q2-P1 MFEM for Incompressible Nonlinear Elasticity Problems. Numerical Mathematics: Theory, Methods and Applications. 12 (4). 995-1011. doi:10.4208/nmtma.OA-2018-0087
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