Fang Wang

Wenbin Chen, Fang Wang, Yanqiu Wang

A family of weak Galerkin finite element discretization is developed for solving the coupled Darcy-Stokes equation. The equation in consideration admits the Beaver-Joseph-Saffman condition on the interface. By using the weak Galerkin approach, in the discrete space we are able to impose the normal continuity of velocity explicitly. Or in other words, strong coupling is achieved in the discrete space. Different choices of weak Galerkin finite element spaces are discussed, and error estimates are given.

Rujing Yao, Yang Wu, Chenghao Wang et al.

Large Language Models (LLMs) have achieved impressive results across numerous domains, yet they experience notable deficiencies in legal question-answering tasks. LLMs often generate generalized responses that lack the logical specificity required for expert legal advice and are prone to hallucination, providing answers that appear correct but are unreliable. Retrieval-Augmented Generation (RAG) techniques offer partial solutions to address this challenge, but existing approaches typically focus only on semantic similarity, neglecting the logical structure essential to legal reasoning. In this paper, we propose the Logical-Semantic Integration Model (LSIM), a novel supervised framework that bridges semantic and logical coherence. LSIM comprises three components: reinforcement learning predicts a structured fact-rule chain for each question, a trainable Deep Structured Semantic Model (DSSM) retrieves the most relevant candidate questions by integrating semantic and logical features, and in-context learning generates the final answer using the retrieved content. Our experiments on a real-world legal QA dataset-validated through both automated metrics and human evaluation-demonstrate that LSIM significantly enhances accuracy and reliability compared to existing methods.