p-Version of the Finite Element Method for Elliptic Equations of Order 2l

摘要

The finite element method has three versions: the h-version, the p-version and the h-p version. In the h-version, increased accuracy is achieved by decreasing the mesh size h while keeping p, the degree of elements used fixed (usually p = 1,2,3). In the p-version, a fixed mesh is used while the degree p of elements are either uniformly or selectively increased to achieve accuracy. The h-p version is a combination of both. The standard h-version has been thoroughly investigated and many commercial and research programs are available. The p- and h-p versions are recent developments. There is only one commercial code, the system PROBE, and the first papers discussing theoretical aspects appeared only in 1981. The approximations of solutions of elliptic problems of order 21 over two - dimensional polygonal domains by the p-version of the finite element is investigated. Optimal rates of convergence are established for the case when elements possessing C continuity are used.