Matched GkGk-constructions always yield CkCk-continuous isogeometric elements

•A construction principle for engineering analysis elements is formally verified.•The principle yields isogeometric CkCk elements from GkGk-manifold constructions.•The manifold representations can have irregular (extraordinary, star)points.•The principle applies in any number of variables and any number of range dimensions.•As a consequence, GkGk-constructions can directly be used to solve PDEs on manifolds

GkGk (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 GkGk constructions for geometry and analysis automatically yield CkCk isogeometric elements. This provides a formal framework for the existing and any future isogeometric elements based on geometric continuity.

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