A note on the polynomial approximation of vertex singularities in the boundary element method in three dimensions (Q732339)

The author analyses the polynomial approximations of vertex singularities inherent to solutions of boundary integral equations on a Lipschitz polyhedral surface. In particular, approximations of singularities of the type \(r^\lambda|\log r|^\beta\) is studied, where \(\lambda> -1/2\). The main result provides an error estimate (in terms of the mesh parameter \(h\) and polynomial degree \(p\)) for the approximation of vertex singularities by piecewise polynomials on quasi-uniform meshes.