Radiative corrections in highly charged ions and tests of QED in strong electric and magnetic fields

To provide predictions of the Lamb shift of highly charged ions on the leve l of accuracy of about 10(-6) has been achieved after exact results for the contributions of all two-photon self-energy diagrams have been performed. We report on the present status of our Lamb-shift calculations including al l QED-corrections of first- and second-order in the finestructure constant a and all relevant nuclear effects. An excellent agreement between the most recent experimental data for Lamb shift of the ls-ground state in hydrogen like uranium can be stated. This can serve as a sensitive test of QED in th e strongest electric fields accessible in nature. In a second part of this article we report about an all-order numerical evaluation of the one-photon selfenergy at low nuclear charge (Z = 1,...,5). A sensitive comparison of our numerical approach with analytical approach to the one-photon selfenerg y confirms the consistency of these two different approaches (numerical and analytic) to very high precision.