Inverse Problems, vol. 24 (2008), pp. 034011/1-22.

This article was selected for the Editorial Board Highlights 2008.

Adaptive meshes are therefore an indispensable tool. In this paper, we will describe a framework for the adaptive finite element solution of optical tomography problems. It takes into account all steps starting from the formulation of the problem including constraints on the coefficient, outer Newton-type nonlinear and inner linear iterations, regularization, and in particular the interplay of these algorithms with discretizing the problem on a sequence of adaptively refined meshes.

We will demonstrate the efficiency and accuracy of these algorithms on a set of numerical examples of clinical relevance related to locating lymph nodes in tumor diagnosis.