会议摘要（Abstract）

English: The theme of this workshop is “Advanced Numerical Schemes for Multiphysics Problems,” with a dedicated focus on adaptive numerical methods driven by a posteriori error estimates and multiscale methods for complex systems involving physical phenomena. The event will convene internationally renowned scholars in applied mathematics to present breakthroughs in error control for adaptive algorithms, hybrid multiscale frameworks, and their potential applications. The workshop will foster in-depth dialogue on cutting-edge strategies to enhance accuracy, efficiency, and scalability in multiphysics simulations. By uniting theoretical insights with practical challenges, this event aims to significantly advance the exchange of cutting-edge research trends, stimulate interdisciplinary collaboration, and empower participants—particularly early-career researchers—with innovative tools to address pressing scientific problems. 

中文：本次研讨会的主题为“多物理场问题的先进数值方法”，重点关注基于后验误差估计的自适应数值方法以及面向复杂多物理系统的多尺度建模技术。 本次活动将汇聚国际知名应用数学家，共同探讨自适应算法误差控制、多尺度耦合框架及其潜在应用领域的最新突破。研讨会将围绕提升多物理场模拟精度、效率与可扩展性的前沿策略展开深入对话，通过连接理论创新与实际挑战，推动尖端研究趋势的交流、促进跨学科合作，并助力青年科研人员掌握创新工具以应对重大科学难题。 

举办意义(Description of the aim)

English: The numerical simulation of multiphysics problems, characterized by physical phenomena across disparate scales, poses significant theoretical and computational challenges. For systems amenable to derive the a posteriori error estimates, adaptive algorithm strategies can rigorously quantify and control numerical approximation accuracy, optimizing computational efficiency. However, for problems dominated by multiscale interactions鈥攕uch as those involving heterogeneous materials, fluid-structure coupling, or reactive transport鈥攖raditional error frameworks often fail to resolve cross-scale dependencies, necessitating novel multiscale or reduced-order methodologies. This workshop aims to unite experts in adaptive algorithms driven by a posteriori error estimates and multiscale numerical schemes to collaboratively address these dual challenges. By fostering dialogue between theorists developing rigorous a posteriori error estimators and practitioners designing scalable multiscale solvers, the event will advance robust, high-fidelity computational tools for multiphysics applications in geosciences, electromagnetism, energy systems, and biomechanics. The discussions will not only bridge gaps between methodology and implementation but also underscore the practical significance of cutting-edge numerical strategies in addressing real-world engineering and scientific challenges. numerical strategies in addressing real-world engineering and scientific challenges. 

中文：多物理场问题的数值模拟因其跨尺度物理现象的特征，在理论与计算层面均带来巨大挑战。 对于可建立后验误差估计的物理系统，自适应算法策略能够严格量化并控制数值逼近精度，从而优化计算效率。然而，在以多尺度相互作用为主导的问题中（如涉及非均质材料、流固耦合或反应输运的体系），传统误差分析框架往往难以解析跨尺度关联，亟需发展新型多尺度或降阶方法。本次研讨会旨在联合后验误差估计驱动的自适应算法与多尺度数值方法领域的专家，共同应对上述双重挑战。通过促进后验误差估计理论研究者与可扩展多尺度求解器开发者之间的深度对话，本次活动将推动地球科学、电磁学、能源系统及生物力学等领域多物理场应用的鲁棒高保真计算工具发展。相关讨论不仅将架起方法论与工程实践之间的桥梁，更将突显前沿数值策略在解决实际科学与工程难题中的重大意义。