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Error analysis of quadrilateral Wilson element for Reissner-Mindlin plate. (English) Zbl 1169.74609

Summary: We generalize the rectangular nonconforming Wilson element method proposed by Z. Zhang and S. Zhang [Wilson element for the Reissner-Mindlin plate, ibid. 113, 55–65 (1994; Zbl 0847.73070)] for the Reissner-Mindlin plate problem to the general quadrilateral mesh and analyze the error. It is proved that this method converges at uniformly optimal rates with respect to both the energy and \(L^{2}\) norms. These estimates improve those of [loc. cit.] in the sense that the requirement of \(H^{3}(\Omega )\) regularity on the solution is dropped, and that the \(L^{2}\) error estimate of this scheme is analyzed. The numerical examples at the end of this paper demonstrate the superiority of this method over the MITC4 [K.-J. Bathe and E. N. Dvorkin, Int. J. Numer. Methods Eng. 21, 367–383 (1985; Zbl 0551.73072)].

MSC:

74S05 Finite element methods applied to problems in solid mechanics
74K20 Plates
65N15 Error bounds for boundary value problems involving PDEs
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