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Volume 21, Issue 6
Discrete Minus One Norm Least-Squares for the Stress Formulation of Linear Elasticity with Numerical Results

Sang Dong Kim, Byeong Chun Shin, Seokchan Kim & Gyungsoo Woo

J. Comp. Math., 21 (2003), pp. 689-702.

Published online: 2003-12

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  • Abstract

This paper studies the discrete minus one norm least-squares methods for the stress formulation of pure displacement linear elasticity in two dimensions. The proposed least-squares functional is defined as the sum of the $L^2-$ and $H^{-1}-$norms of the residual equations weighted appropriately. The minus one norm in the functional is replaced by the discrete minus one norm and then the discrete minus one norm least-squares methods are analyzed with various numerical results focusing on the finite element accuracy and multigrid convergence performances.

  • Keywords

$H^{-1}$ least-squares, Linear elasticity, Multigrid method.

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COPYRIGHT: © Global Science Press

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@Article{JCM-21-689, author = { Sang Dong Kim, Byeong Chun Shin, Seokchan Kim and Gyungsoo Woo }, title = {Discrete Minus One Norm Least-Squares for the Stress Formulation of Linear Elasticity with Numerical Results}, journal = {Journal of Computational Mathematics}, year = {2003}, volume = {21}, number = {6}, pages = {689--702}, abstract = {

This paper studies the discrete minus one norm least-squares methods for the stress formulation of pure displacement linear elasticity in two dimensions. The proposed least-squares functional is defined as the sum of the $L^2-$ and $H^{-1}-$norms of the residual equations weighted appropriately. The minus one norm in the functional is replaced by the discrete minus one norm and then the discrete minus one norm least-squares methods are analyzed with various numerical results focusing on the finite element accuracy and multigrid convergence performances.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/8890.html} }
TY - JOUR T1 - Discrete Minus One Norm Least-Squares for the Stress Formulation of Linear Elasticity with Numerical Results AU - Sang Dong Kim, Byeong Chun Shin, Seokchan Kim & Gyungsoo Woo JO - Journal of Computational Mathematics VL - 6 SP - 689 EP - 702 PY - 2003 DA - 2003/12 SN - 21 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/8890.html KW - $H^{-1}$ least-squares, Linear elasticity, Multigrid method. AB -

This paper studies the discrete minus one norm least-squares methods for the stress formulation of pure displacement linear elasticity in two dimensions. The proposed least-squares functional is defined as the sum of the $L^2-$ and $H^{-1}-$norms of the residual equations weighted appropriately. The minus one norm in the functional is replaced by the discrete minus one norm and then the discrete minus one norm least-squares methods are analyzed with various numerical results focusing on the finite element accuracy and multigrid convergence performances.

Sang Dong Kim, Byeong Chun Shin, Seokchan Kim and Gyungsoo Woo . (2003). Discrete Minus One Norm Least-Squares for the Stress Formulation of Linear Elasticity with Numerical Results. Journal of Computational Mathematics. 21 (6). 689-702. doi:
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