Consider the Poisson equation with homogeneous Dirichlet boundary conditions on a
polygonal domain with one reentrant corner. In this paper, we develop a new finite element
method for the accurate computation of the solution and stress intensity factors. It is well
known that the solution of such a problem has a singular function representation: u=w+ληs,
where w∈H^2(Ω)∩H^1_0(Ω), λ∈\calR and η are the stress intensity factor and cut-off
function, respectively, and s is a known singular function depending only on the reentrant …

Abstract In Cai and Kim (SIAM J. Numer. Anal. 2001; 39: 286), we developed and analysed
a new accurate finite element method using singular functions for the Poisson equation on a
two‐dimensional polygonal domain with re‐entrant corners. This method first computes the
regular part of the solution, then stress intensity factors, and finally the solution itself. This
note extends this method to the Poisson equation on a domain with cracks and considers a
higher‐order method when f∈ H1 (Ω). Copyright© 2002 John Wiley & Sons, Ltd.