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Superconvergence in the projected‐shear plate‐bending finite element method
Author(s) -
Zhang Zhimin
Publication year - 1998
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/(sici)1098-2426(199805)14:3<367::aid-num6>3.0.co;2-k
Subject(s) - superconvergence , mathematics , bilinear interpolation , finite element method , norm (philosophy) , mathematical analysis , shear (geology) , geometry , structural engineering , geology , petrology , statistics , political science , law , engineering
A projected‐shear finite element method for periodic Reissner–Mindlin plate model are analyzed for rectangular meshes. A projection operator is applied to the shear stress term in the bilinear form. Optimal error estimates in the L 2 ‐norm, the H 1 ‐norm, and the energy norm for both displacement and rotations are established and gradient superconvergence along the Gauss lines is justified in some weak senses. All the convergence and superconvergence results are uniform with respect to the thickness parameter t . © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 367–386, 1998