Finite Hyperelements - a 4D Geometrical Framework Using Covariant Bases and Metric Tensors

A method is presented to evaluate space-time finite element matrices in a general 4D context. Unlike the classical Jacobian-based 'textbook' approach, the method described herein uses curvilinear gradient operators to properly handle finite elements having fewer local dimensions (i.e. two or three) than the global embedding domain. This unconventional, but powerful, method is described in details and is illustrated by an application simulating 4D pure convection in a curved diverging-converging flow field.