Applied Mathematics and Mechanics (English Edition) ›› 1986, Vol. 7 ›› Issue (5): 443-459.

• Articles • Previous Articles     Next Articles

ON THE COMPACTNESS OF QUASI-CONFORMING ELEMENT SPACES AND THE CONVERGENCE OF QUASI-CONFORMING ELEMENT METHOD

Zhang Hong-qing, Wang Mingi   

  1. Department of Applied Mathematics, Dalian Institute of Technology, Dalian
  • Received:1985-03-05 Online:1986-05-18 Published:1986-05-18

Abstract: In this paper, the compactness of quasi-conforming element spaces and the convergence of quasi-conforming element method are discussed. The well-known Rellich compactness theorem is generalized to the sequences of quasi-conforming element spaces with certain properties, and the generalized Poincare inequality. The generalized Friedrichs inequality and the generalized inequality of Poincare-Friedrichs are proved true for them. The error estimates are also given. It is shown that the quasi-conforming element method is convergent if the quasi-conforming element spaces have the approximability and the strong continuity, and satisfy the rank condition of element and pass the test IPT. As practical examples, 6-paramenter, 9-paramenter, 12-paramenter, 15-parameter, 18-parameter and 21-paramenter quasi-conforming elements are shown to be convergent, and their L2'2errorsare0(hτ), 0(hτ),0(hτ2),O(hτ2). 0(hτ2) , and 0(hτ4) respectively.

Key words: rotating composite cylinder, orthotropic, heterogeneous, variable-thickness, fiber-reinforced viscoelastic core

APS Journals | CSTAM Journals | AMS Journals | EMS Journals | ASME Journals