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Volume 7, Issue 4
Error Estimates of Morley Triangular Element Satisfying the Maximal Angle Condition

S. Mao, S. Nicaise & Z.-C. Shi

Int. J. Numer. Anal. Mod., 7 (2010), pp. 639-655.

Published online: 2010-07

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  • Abstract

In this paper, we establish the convergence of a nonconforming triangular Morley element for the plate bending problem on degenerate meshes. An explicit bound for the interpolation error is derived for arbitrary triangular meshes without any assumptions. The optimal convergence rates of the moment error and rotation error are derived for triangular meshes satisfying the maximal angle condition. Our results can also be extended to the three dimensional Morley element presented recently in [41]. Finally, some numerical results are reported that confirm our theoretical results.

  • Keywords

Morley element, plate elements, plate bending problems, maximal angle condition.

  • AMS Subject Headings

65N12, 65N15, 65N30, 65N50

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-7-639, author = {Mao , S.Nicaise , S. and Shi , Z.-C.}, title = {Error Estimates of Morley Triangular Element Satisfying the Maximal Angle Condition}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2010}, volume = {7}, number = {4}, pages = {639--655}, abstract = {

In this paper, we establish the convergence of a nonconforming triangular Morley element for the plate bending problem on degenerate meshes. An explicit bound for the interpolation error is derived for arbitrary triangular meshes without any assumptions. The optimal convergence rates of the moment error and rotation error are derived for triangular meshes satisfying the maximal angle condition. Our results can also be extended to the three dimensional Morley element presented recently in [41]. Finally, some numerical results are reported that confirm our theoretical results.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/743.html} }
TY - JOUR T1 - Error Estimates of Morley Triangular Element Satisfying the Maximal Angle Condition AU - Mao , S. AU - Nicaise , S. AU - Shi , Z.-C. JO - International Journal of Numerical Analysis and Modeling VL - 4 SP - 639 EP - 655 PY - 2010 DA - 2010/07 SN - 7 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/743.html KW - Morley element, plate elements, plate bending problems, maximal angle condition. AB -

In this paper, we establish the convergence of a nonconforming triangular Morley element for the plate bending problem on degenerate meshes. An explicit bound for the interpolation error is derived for arbitrary triangular meshes without any assumptions. The optimal convergence rates of the moment error and rotation error are derived for triangular meshes satisfying the maximal angle condition. Our results can also be extended to the three dimensional Morley element presented recently in [41]. Finally, some numerical results are reported that confirm our theoretical results.

S. Mao, S. Nicaise & Z.-C. Shi. (1970). Error Estimates of Morley Triangular Element Satisfying the Maximal Angle Condition. International Journal of Numerical Analysis and Modeling. 7 (4). 639-655. doi:
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