A new family of finite elements: the pyramidal elements

The key step in the successful numerical solution of problems by application of finite element analysis (FEA) is the construction of suitable finite dimensional basis functions and basis subspaces. Engineers have a variety of element types to choose from when constructing models for FEA. We present and test a new and original element, the pyramidal element, that can be very practical for linking meshes of different types, that is to say hexahedrons, tetrahedrons and prisms. This element type is unused in finite element packages because of its unfamiliar property: its nonpolynomial shape functions. To validate these new elements with classic finite elements, we study a simple problem with the Flux3D package, meshed in different types of elements: a 3D cylindrical capacitor. Dirichlet conditions are applied to the internal surface and the external surface of the cylinder in order to create an electric field. The electrical potential V is used for the FE calculation.