The parallel vectors (PV) operator is a feature extraction approach for defining line-type features such as creases (ridges and valleys) in scalar fields, as well as separation, attachment, and vortex core lines in vector fields. In this work, we extend PV feature extraction to higher-order data represented by piecewise analytical functions defined over grid cells. The extraction uses PV in two distinct stages. First, seed points on the feature lines are placed by evaluating the inclusion form of the PV criterion with reduced affine arithmetic. Second, a feature flow field is derived from the higher-order PV expression where the features can be extracted as streamlines starting at the seeds. Our approach allows for guaranteed bounds regarding accuracy with respect to existence, position, and topology of the features obtained. The method is suitable for parallel implementation and we present results obtained with our GPU-based prototype. We apply our method to higher-order data obtained from discontinuous Galerkin fluid simulations.