  The solution of the elliptic partial differential equation has interface
singularity at the points which are either the intersections of interfaces or
the intersections of interfaces with the boundary of the domain. The
singularities that arises in the elliptic interface problems are very complex.
In this article, we propose an exponentially accurate nonconforming spectral
element method for these problems based on [7, 18]. A geometric mesh is used in
the neighbourhood of the singularities and the auxiliary map of the form
$z=ln\xi$ is introduced to remove the singularities. The method is essentially
a least-squares method and the solution can be obtained by solving the normal
equations using the preconditioned conjugate gradient method (PCGM) without
computing the mass and stiffness matrices. Numerical examples are presented to
show the exponential accuracy of the method.
