Curvilinear Vector Finite Elements Using a Set of Hierarchical Basis Functions

Curvilinear finite elements are developed employing a second order geometrical mapping and implemented for a set of hierarchical vector basis functions of up to full second order. The development covers the computation of the mass and stiffness matrices and the geometrical transformation from the real curvilinear element to the rectilinear reference element with the basis functions and their curls tabulated in reference coordinates up to full second order. The postprocessing of results for curvilinear elements is also discussed. The use of these elements is illustrated by applying them to scattering and eigenanalysis problems involving conducting spheres. The improvement in the accuracy of the solution is demonstrated by comparing the error in the results obtained using curvilinear elements to those obtained using rectilinear elements