  A finite-element discretization of such an equation yields a linear system
whose conditioning worsens as the variations in the values of PDE coefficients
becomes large. This paper introduces a procedure by which the discrete system
obtained from a linear finite element discretization of the given continuum
problem is converted into an equivalent linear system of the saddle point type.
Then a robust preconditioner for the Lanczos method of minimized iterations for
solving the derived saddle point problem is proposed. Robustness with respect
to the contrast parameter and the mesh size is justified. Numerical examples
support theoretical results and demonstrate independence of the number of
iterations on the contrast, the mesh size and also on the different contrasts
on the inclusions.
