AbstractThe method of flux synthesis is extended in a systematic way to allow the possibility of using different sets of trial functions in different axial zones. The necessary equations are derived in some detail and numerical examples are presented. The results of these examples are very satisfactory and suggest, therefore, that the synthesis procedure can be made much more useful and powerful by extending it in this way. In a more general context they suggest that the basic notation of deriving discontinuous-type approximation methods from an appropriate variational principle is a valid and very effective idea.