Matched Gk-constructions always yield Ck-continuous isogeometric elements

Gk (geometrically continuous surface) constructions were developed to create surfaces that are smooth also at irregular points where, in a quad-mesh, three or more than four elements come together. Isogeometric elements were developed to unify the representation of geometry and of engineering analysis. We show how matched Gk constructions for geometry and analysis automatically yield Ck isogeometric elements. This provides a formal framework for the existing and any future isogeometric elements based on geometric continuity.