In this paper, a novel approach that allows to use p-adaptation with continuous finite elements is proposed. Under certain conditions, primarily the use of a residual distribution scheme, it is possible to avoid the continuity constraint imposed to the approximate solution, while still retaining the advantages of a method using continuous finite elements. The theoretical material, the complete numerical method and practical results show as a proof of concept that p-adaptation is possible with continuous finite elements, well suited for non linear cases and that this approach brings some advantages.