The Rate of Divergence of Hypercubic Pyramidal Elements
Journal "Fundamental Sciences and Applications"


rate of divergence, measure of degeneracy, n-dimensional pyramidal elements, canonical domains.×


The earliest papers on applications of the finite element method for solving partial differential equations were related to one-dimensional problems. In the present day, the finite element method has been successfully applied for solving boundary and eigenvalue problems in higher-dimensional Euclidean spaces. The minimal measure of degeneracy of the simplicial elements depends on the dimension of the finite space. It tends to infinity when the dimension of the Euclidean space grows up unbounded. The pyramidal elements are relatively new compared to hexahedral and simplicial elements. The major role of the pyramids is to assure conforming coupling between structured and unstructured finite element meshes. This paper deals with the rate of divergence of the sequence of pyramidal finite elements. Detailed proofs of two divergence theorems are obtained. For illustrations, the results of the theorems are presented graphically.