中文摘要：

自适应网格方法是科学与工程应用中的关键技术之一。基于拉格朗日方法计算过程中网格的处理方式，论述了耦合型和后处理型两种自适应网格类型。在耦合型自适应网格方法下，论述了网格细化技术、移动网格和自适应坐标法。在后处理型自适应网格方法下。描述了网格重分、邻域重连、邻域可变和邻域优化等自适应网格技术。对各种自适应网格方法的基本理论、效果、适应物理特征能力和特色等优缺点进行了分析与对比。为使自适应网格技术真正走向科学与工程领域提供了参考。

英文摘要：

Adaptive grid method is one of the key techniques in the area of science and engineering applications. Based on the Lagrange grids of computational method, two types of different adaptive grid methods including couple adaptive mesh methods and pro-processor adaptive mesh methods are described. In the framework of couple adaptive mesh methods, several adaptive mesh methods including adaptive mesh refinement, moving mesh method, and adaptive coordinate methods are reviewed. In the framework of pro-processor adaptive mesh methods, adaptive mesh redistribution, reconnection-based method, changing connectivity of the mesh, and connectivity optimization method are described. Their advantages and disadvantages are compared with each other and analyzed with regard to the basic theory, efficiency, robustness for physics characteristics, and other features. It provides the support for using adaptive mesh method in the area of science and engineering applications.