The application of the multigrid method MGD1 for the efficient and stable simulation of electrochemical transport problems is described. The approach is illustrated by its application to the simulation of double electrode problems, thought not to be readily tractable by other approaches. In particular the reverse collection efficiency is successfully simulated in addition to the modelling of conventional double electrode problems. In the reverse case, material generated on a downstream electrode in a double channel electrode system diffuses upstream against the direction of the convective flow to a detector electrode, whereas conventionally the generator electrode is located upstream. The dependence of the collection efficiency (defined as the ratio of the detector to generator electrode current) on the cell geometry and solution flow rate is established and reported.