Energy-based methods are highly successful and accurate approaches to calculate the optical flow between images. If discontinuity preservation and robustness against image noise and local illumination changes are required, a particularly appealing variational formulation for optical flow is based on Total Variation (TV) regularization and on the robust L1 data fidelity norm. In this work we present a novel minimization approach to determine the optical flow using a TV-L1 energy functional. Our proposed method results in very efficient numerical scheme, which can be additionally accelerated by modern graphics processing units. Thus, we can demonstrate the real-time performance of our approach for video inputs at a resolution of 320 x 240 pixels.