Adapting For Moving Boundary Problems

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.