Additional overlapping finite elements – The pyramid and prism elements

•Two new overlapping finite elements are presented: a pyramid element and a prism element.•The elements are compatible with overlapping brick and tetrahedral elements.•When used as coupling elements, they are also compatible with the traditional finite elements.•The elements contain no spurious zero energy mode and pass the patch tests.•The elements are shown to be quite insensitive to element distortions; convergence tests are given.•Illustrative applications using the AMORE scheme with the new overlapping elements are presented. 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 providing the possibility to transition between other overlapping and traditional elements. Both new overlapping 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 elements 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 overlapping elements are employed.