A mixed high-order vector finite element method for waveguides: Convergence and spurious mode studies

In this article we construct and analyse the performance of various combinations of high order edge elements for the transverse field component with high order node elements for the longitudinal field component. The overall efficiency and mode resolution improve dramatically with high order elements. For example, quadratic/cubic elements provide accuracy of 10(-4) in eigenvalue 1000 times faster and resolve the discontinuities in the field very accurately. In the mixed FEM for waveguides we observed that edge elements may produce spurious modes. When the order of the edge elements is equal or larger than the order of the node elements, spurious and degenerate modes are present. Any other combination of the orders did not produce spurious modes. We study the spurious modes from the divergence point of view. We also study the convergence properties of high order elements and compare the results with the theory. Copyright (C) 2005 John Wiley & Sons, Ltd.