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View adaptation relies on adapting a set of materialized views in response to schema changes of source relations and/or after view redefinition. Recently, several view selection methods that are based on materializing fragments of the view rather than the whole view have been proposed. We call this approach the fragment-based approach. This paper presents a view adaptation method in the fragment-based approach, which is aimed at exploiting the opportunities to share not only materialized data, but also computation between the different views. In order to do this, the views are modeled using the so-called multiview materialization graph, which represents the views as a bipartite directed acyclic graph whose nodes are operations and fragments of the views. Then, the adaptation is performed regarding all materialized views and not solely the old materialization of the view. However, the data independence is preserved for the views that are not affected by the change. On the contrary, in related work, the adaptation technique is based solely on the old materialization of the same view. We studied the impact of the fragmentation on the adaptation techniques and showed the advantages and drawbacks of this approach.