Local Citation Recommendation is a task that finds the missing reference in the corresponding citation placeholder. It is mainly contextual since context identifies the citation. On the other hand, a context can be a descriptor for a set of papers. In other words, there can be more than one candidate citation for a context. Thus, a further matching of a context with candidate papers is beneficial. Titles and abstracts of candidate papers serve as a global context to match with the local one. This work proposes a state-of the-art approach for the Local Citation Recommendation task that exploits the similaritiesbetween global and local contexts to generate citation predictions. By utilizing a Graph Convolutional Network (GCN) with BERT embeddings, our proposed model demonstrates superior performance over previous methods. It not only outperforms all prior approaches on the benchmark datasets of ACL-200, FullTextPeerRead, RefSeer, and arXiv but also strikes a balance between speed, memory, and computational requirements. Once deployed as a production-level Local Citation Recommendation, it is fast enough to enable real-time recommendations for researchers.