Incorporation of contact for high-order finite elements in covariant form

The covariant contact description is applied to incorporate the treatment of contact problems into a high-order finite element technique. A hierarchical enrichment of the shape functions space allows to construct a contact layer finite element combining both exact geometry representation for contact surfaces, and a mesh with linear shape functions for the interior of the contacting bodies. The developed contact approach can be viewed as a smoothing technique for linear meshes as well as a general application of high-order FEM. The good approximation property for the developed contact layer elements is shown for the classical Hertz problem even within a few contact elements discretizing the contact zone.