Natural SciencesCivil EngineeringTopologyArithmetic Geometry
. Conforming finite elements in H(div;\\Omega\\Gamma and H(curl; \\Omega\\Gamma can be regarded as discrete differential forms (Whitney--forms). The construction of such forms is based on an interpolation idea, which boils down to a simple extension of the differential form to the interior of elements. This flexible approach can accommodate elements of more complicated shapes than merely tetrahedra and bricks. The pyramid serves as an example for the successful application of the construction: New Whitney forms are derived for it. Key words. Whitney elements, edge elements, pyramidal element AMS subject classifications. 65N30 41A10 58A15 1. Introduction. The true meaning of differential operators like div and curl is only revealed when they are looked at from the perspective of differential forms. In many cases, the calculus of differential forms is a very natural and powerful tool to express the partial differential equations arising from mathematical modeling of physical phenomena. ...