Zhang Hong-qing, Wang Ming. On the Compactness of Quasi-Conforming Element Spaces and the Convergence of Quasi-Conforming Element Method[J]. Applied Mathematics and Mechanics, 1986, 7(5): 409-423.
 Citation: Zhang Hong-qing, Wang Ming. On the Compactness of Quasi-Conforming Element Spaces and the Convergence of Quasi-Conforming Element Method[J]. Applied Mathematics and Mechanics, 1986, 7(5): 409-423.

# On the Compactness of Quasi-Conforming Element Spaces and the Convergence of Quasi-Conforming Element Method

• Publish Date: 1986-05-15
• In this paper,the compactness of quasi-conforming clement spices 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 generalzed 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 test IPT.As practical examples,6-parameter,9-parameter,12-parameter,15-parameter,18-parameter and 21-parameter quasi-conforming elements are shown to be convergent,and tlieir.L2,2(Ω)-errors are O(hτ)、O(hτ)、O(hτ2)、O(hτ2)、O(hτ3)and O(hτ4)respectively.
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