Numerical evaluation of hierarchical vector finite elements on curvilinear domains in 2-D

When using the finite element method, computational efficiency may be improved by using higher order elements. Typical 2-D triangular rectilinear elements cannot exactly model curved geometries, negating the advantage of higher order elements when such geometries are modeled. Curvilinear elements can be applied to such problems, and have significantly better computational efficiency than rectilinear elements when higher order elements are used. Results are shown for elemental basis orders ranging from CT/LN through full fifth order in rectilinear and curvilinear domains.