Adapting For Moving Boundary Problems

该项目旨在开发和分析解决移动边界问题的强大而有效的数值技术。最近的有限元方法（虚元法、不连续伽辽金法）基于非常一般的网格，将以自适应的方式加以利用。网格灵活性允许复杂几何图形的有效分辨率，特别是在移动域的存在。此外，一般网格元素允许移动边界/界面的局部分辨率，而不需要先验的拟合网格。将考虑的重要应用示例包括移动界面问题和流固相互作用问题。将深入研究的一个重要方面是在拉格朗日型网格节点运动中结合自适应框架来解决运动域/扩展现象问题。

This project aims at developing and analysing robust and efficient numerical techniques for the solution of moving boundary problems. Recent Finite Element approaches (Virtual Element Methods, discontinuous Galerkin Methods) based on very general meshes will be exploited in an adaptive fashion. Mesh flexibility permits effective resolution of complex geometries, particularly in presence of moving domains. In addition, general mesh elements permit local resolution of moving boundaries/interfaces without the need of a priori fitted meshes. Examples of important applications that will be considered include moving interface problems and fluid-structure interaction problems.One important aspect which will be thoroughly investigated is the incorporation of the adaptive framework within Lagrangian-type mesh-node movement for problems on moving domains/expansion phenomena.