On the FEM treatment of wedge singularities in waveguide problems

This paper introduces a novel extension to a scalar two-dimensional polynom ial finite-element basis to better cope with wedge singularities in wavegui de problems. An error estimate for the computed cutoff frequencies of the w aveguide shows that the relative H-1 error of the modal solution is critica l, We demonstrate that the present extension significantly improves the app roximation properties of a polynomial basis, especially in the H-1 norm. Nu merical examples show that the present extension compares well with other r ecent techniques. Combining variable order elements with singular basis ext ension provides further significant reduction of the computational burden.