On the FEM treatment of wedge singularities in waveguide problems

This paper introduces a novel extension to a scalar two-dimensional polynomial finite-element basis to better cope with wedge singularities in waveguide problems. An error estimate for the computed cutoff frequencies of the waveguide shows that the relative H ¹ error of the modal solution is critical. We demonstrate that the present extension significantly improves the approximation properties of a polynomial basis, especially in the H¹ norm. Numerical examples show that the present extension compares well with other recent techniques. Combining variable order elements with singular basis extension provides further significant reduction of the computational burden