Non-linear Electrical Impedance Tomography (EIT) is a novel technique for non-invasive and cost-effective imaging, which makes it an optimal candidate for medical applications. The basic principles of EIT can be derived from Maxwell's Equations. These need to be solved numerically within the object under investigation using, for example, a finite element mesh. To solve the ill-conditioned inverse problem on this finite discretization, additional constraints have to be applied. In addition, the speed of reconstruction plays an important role and limits number and size of the used elements. The developed self-adaptive mesh refinement algorithm reduces - based on an a posteriori energy error estimate - the number of elements required for an accurate solution compared to conventional uniform meshing techniques. The gained speed-up in the image formation process enhances the potential use of EIT in medical real-time imaging.