Comparison of scalar and vector FEM forms in the case of an elliptic cylinder

An invariant vector approximation of unknown quantities is proposed and implemented to construct the stiffness matrix of a quadrilateral curved finite element in the form of a fragment of the mid-surface of an elliptic cylinder with 18 degrees of freedom per node. Numerical examples show that the vector approximation has significant advantages over the scalar one as applied to arbitrary shells with considerable mid-surface curvature gradients.