Adapting For Moving Boundary Problems

该项目旨在开发和分析用于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（虚拟单元法，不连续伽辽金法）的基础上非常一般的网格将利用自适应的方式。网格的灵活性允许复杂的几何形状的有效解决方案，特别是在移动域的存在。此外，一般的网格元素允许移动边界/接口的局部分辨率，而不需要先验拟合网格。将被考虑的重要应用的例子包括移动界面问题和流体-结构相互作用问题。一个重要的方面，这将是彻底调查的拉格朗日型网格节点运动的问题上移动域/膨胀现象的自适应框架的结合。

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.