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Volume 1, Issue 1
A Superconvergent Finite Element Scheme for the Reissner-Mindlin Plate by Projection Methods

J. Wang & X. Ye

Int. J. Numer. Anal. Mod., 1 (2004), pp. 99-110.

Published online: 2004-01

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  • Abstract

The Reissner-Mindlin model is frequently used by engineers for plates and shells of small to moderate thickness. This model is well known for its "locking" phenomenon so that many numerical approximations behave poorly when the thickness parameter tends to zero. Following the formulation derived by Brezzi and Fortin, we construct a new finite element scheme for the Reissner-Mindlin model using $L^2$ projections onto appropriately-chosen finite element spaces. A superconvergence result is established for the new finite element solutions by using the $L^2$ projections. The superconvergence is based on some regularity assumption for the Reissner-Mindlin model and is applicable to any stable finite element methods with regular but non-uniform finite element partitions.

  • Keywords

finite element methods, superconvergence, the method of least-squares fitting, Reissner-Mindlin plate.

  • AMS Subject Headings

65F10, 65F30

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-1-99, author = {}, title = {A Superconvergent Finite Element Scheme for the Reissner-Mindlin Plate by Projection Methods}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2004}, volume = {1}, number = {1}, pages = {99--110}, abstract = {

The Reissner-Mindlin model is frequently used by engineers for plates and shells of small to moderate thickness. This model is well known for its "locking" phenomenon so that many numerical approximations behave poorly when the thickness parameter tends to zero. Following the formulation derived by Brezzi and Fortin, we construct a new finite element scheme for the Reissner-Mindlin model using $L^2$ projections onto appropriately-chosen finite element spaces. A superconvergence result is established for the new finite element solutions by using the $L^2$ projections. The superconvergence is based on some regularity assumption for the Reissner-Mindlin model and is applicable to any stable finite element methods with regular but non-uniform finite element partitions.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/968.html} }
TY - JOUR T1 - A Superconvergent Finite Element Scheme for the Reissner-Mindlin Plate by Projection Methods JO - International Journal of Numerical Analysis and Modeling VL - 1 SP - 99 EP - 110 PY - 2004 DA - 2004/01 SN - 1 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/968.html KW - finite element methods, superconvergence, the method of least-squares fitting, Reissner-Mindlin plate. AB -

The Reissner-Mindlin model is frequently used by engineers for plates and shells of small to moderate thickness. This model is well known for its "locking" phenomenon so that many numerical approximations behave poorly when the thickness parameter tends to zero. Following the formulation derived by Brezzi and Fortin, we construct a new finite element scheme for the Reissner-Mindlin model using $L^2$ projections onto appropriately-chosen finite element spaces. A superconvergence result is established for the new finite element solutions by using the $L^2$ projections. The superconvergence is based on some regularity assumption for the Reissner-Mindlin model and is applicable to any stable finite element methods with regular but non-uniform finite element partitions.

J. Wang & X. Ye. (1970). A Superconvergent Finite Element Scheme for the Reissner-Mindlin Plate by Projection Methods. International Journal of Numerical Analysis and Modeling. 1 (1). 99-110. doi:
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