A general approach to the construction of nonconforming finite elements on convex polytopes

This paper establishes a general approach for constructing a new class of nonconforming finite elements on arbitrary convex polytope. Our contributions generalize or complete several well-known nonconforming finite elements such as: the Crouzeix–Raviart triangle element, the Han parallelogram element, the nonconforming rotated parallelogram element of Rannacher and Turek, and several others.