Additional overlapping finite elements - The pyramid and prism elements

Our objective in this paper is to present two new overlapping finite elements: a pyramid element and a prism element. These elements are useful when meshing general three-dimensional geometries in pro-viding the possibility to transition between other overlapping and traditional elements. Both new over-lapping elements are compatible with overlapping brick and tetrahedral elements, and when used as coupling elements also with the traditional finite elements. We theoretically formulate the two new overlapping finite elements, show that only the rigid body modes correspond to zero eigenvalues (hence the elements contain no spurious zero energy mode), show that the patch test is passed, and test the ele-ments for their convergence behavior and condition numbers. We also show that the elements are quite insensitive to element distortions and revisit the imposition of displacement boundary conditions. Finally, we give some illustrative applications using the AMORE scheme in which also the new overlap-ping elements are employed.(c) 2022 Elsevier Ltd. All rights reserved.

Automated summary

The objective of this paper is to introduce two new overlapping finite elements and validate their properties and applications. These new elements can be utilized for meshing three-dimensional geometries, providing transitional capabilities, and compatibility with other elements.