Vector finite elements for electromagnetic field computation

A novel structure for the finite-element analysis of vector fields is presented. This structure uses the affine transformation to represent vectors and vector operations over triangular domains. Two-dimensional high-order vector elements are derived that are consistent with Whitney forms. One-form elements preserve the continuity of the tangential components of a vector field across element boundaries, while two-form elements preserve the continuity of the normal components. The one-form elements are supplemented with additional variables to achieve pth order completeness in the range space of the curl operator. The resulting elements are called tangential vector finite elements and provide consistent, reliable, and accurate methods for solving electromagnetic field problems.