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Large Language Models (LLMs) have demonstrated significant potential across various applications, but their use as AI copilots in complex and specialized tasks is often hindered by AI hallucinations, where models generate outputs that seem plausible but are incorrect. To address this challenge, we develop AutoFEA, an intelligent system that integrates LLMs with Finite Element Analysis (FEA) to automate the generation of FEA input files. Our approach features a novel planning method and a graph convolutional network (GCN)-Transformer Link Prediction retrieval model, which enhances the accuracy and reliability of the generated simulations. The AutoFEA system proceeds with key steps: dataset preparation, step-by-step planning, GCN-Transformer Link Prediction retrieval, LLM-driven code generation, and simulation using CalculiX. In this workflow, the GCN-Transformer model predicts and retrieves relevant example codes based on relationships between different steps in the FEA process, guiding the LLM in generating accurate simulation codes. We validate AutoFEA using a specialized dataset of 512 meticulously prepared FEA projects, which provides a robust foundation for training and evaluation. Our results demonstrate that AutoFEA significantly reduces AI hallucinations by grounding LLM outputs in physically accurate simulation data, thereby improving the success rate and accuracy of FEA simulations and paving the way for future advancements in AI-assisted engineering tasks.