In this paper, we analyze the perturbation in the reconstructed optical absorption images, resulting from the discretization of the forward and inverse problems. We show that the perturbation due to each problem is a function of both the forward and inverse problem solutions and can be reduced by proper refinement of the discretization mesh. Based on the perturbation analysis, we devise a novel adaptive discretization scheme for forward and inverse problems, which reduces the perturbation on the reconstructed image. Such a discretization scheme leads to an adaptively refined composite mesh sufficient to approximate the forward and inverse problem solutions within a desired level of accuracy while keeping the computational complexity within the computational power limits.