A new Control Volume Finite Element Method for the stable and accurate solution of the drift-diffusion equations on general unstructured grids

► We use edge elements to lift exponentially fitted edge currents into the elements. ► Our approach extends the Scharfetter-Gummel idea to arbitrary unstructured grids. ► The method does not require tunable parameters to handle different features. ► It demonstrates an essentially monotone behavior with minimal under/overshoots. ► Extensive numerical tests confirm the robustness and the accuracy of the new method.