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

In this paper, the compactness of quasi-conforming element spaces and theconvergence of quasi-conforming element method are discussed The well-known Rellichcompactness theorem is generalized to the sequences of quasi-conforming element spaceswith certain properties. and the generalized Poincare inequality.The generalized Friedrichsinequality 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 isconvergent if the quasi-conforming element spaces have the approximability and the strongcontinuity, and satisfy the rank condition of element and pass the test IPT As practicalexamples, 6-paramenter. 9-paramenter, 12-paramenter, 15-parameter, 18-parameter and21-paramenter quasi-conforming elements are shown to be convergent, and theirL(Ω)-errors are O(h)、 O(h)、O(h~2)、O(h~2), O(h~3), and O(h~4) respectively.