Abstract: Based on the distribution characteristic of fields in the neighbourhood of a sharp corner, the B spline finite element method in polar coordinates is exploited for solving the boundary-value problems with singularities at the sharp corner. The proposed method improves the overall accuracy and is convenient to implement. The Motz problem, cracked-beam problem, and eigenvalue problem for the sector waveguides are calculated and analyzed to verify the validity of the method.

Key words: Singularity, polar coordinates, B-spline, finite element