We present numerical simulations of lean hydrogen flames interacting with turbulence. The simulations are performed in an idealized setting using an adaptive low Mach number model with a numerical feedback control algorithm to stabilize the flame. At the conditions considered here, hydrogen flames are thermodiffusively unstable, and burn in cellular structures. For that reason, we consider two levels of turbulence intensity and a case without turbulence whose dynamics is driven by the natural flame instability. An overview of the flame structure shows that the burning in the cellular structures is quite intense, with the burning patches separated by regions in which the flame is effectively extinguished. We explore the geometry of the flame surface in detail, quantifying the mean and Gaussian curvature distributions and the distribution of the cell sizes. We next characterize the local flame speed to quantify the effect of flame intensification on local propagation speed. We then introduce several diagnostics aimed at quantifying both the level of intensification and diffusive mechanisms that lead to the intensification. (C) 2009 The Combustion Institute. Published by Elsevier Inc. All rights reserved.