H(div) and H(curl)-conforming virtual element methods

In the present paper we construct virtual element spaces that are (Formula presented.)-conforming and (Formula presented.)-conforming on general polygonal and polyhedral elements; these spaces can be interpreted as a generalization of well known finite elements. We moreover present the basic tools needed to make use of these spaces in the approximation of partial differential equations. Finally, we discuss the construction of exact sequences of VEM spaces.