I have a rather specific question regarding the condition number. I run FEM simulations which have multiple length scales to them which results in a huge disparity between the largest entries and the smallest entries in my matrix. The condition number can get as high as 10^15 in some circumstances.
In numerical analysis I often see the error bound for the condition number as it applies to error in the computed solution using direct methods. My curiosity is whether this logic applies to error in an iterative-type solver like CG, or GMRES as well. I know that the convergence rate is impacted by the eigenvalues of the matrix, and I do notice huge speed losses when running problems of this type. But, I am uncertain as to the accuracy. Any help would be appreciated.