Domain-specific design patterns provide developers with proven solutions to common design problems that arise, particularly in a target application domain, facilitating them to produce quality designs in the domain contexts. However, research in this area is not mature and there are no techniques to support their detection. Towards this end, we propose a methodology which, when applied on a collection of websites in a specific domain, facilitates the automated identification of domain-specific design patterns. The methodology automatically extracts the conceptual models of the websites, which are subsequently analyzed in terms of all of the reusable design fragments used in them for supporting common domain functionalities. At the conceptual level, we consider these fragments as recurrent patterns consisting of a configuration of front-end interface components that interrelate each other and interact with end-users to support certain functionality. By performing a pattern-based analysis of the models, we locate the occurrences of all the recurrent patterns in the various website designs which are then evaluated towards their consistent use. The detected patterns can be used as building blocks in future designs, assisting developers to produce consistent and quality designs in the target domain. To support our case, we present a case study for the educational domain.