Mats G Larson, Professor, Umeå universitet

郑伟英 研究员

CutFEM: Foundations, Stabilization, and Applications

10月20日（周二）10:00-11:00，蓝白楼311

Cut finite element methods (CutFEM) provide a flexible framework for discretizing partial differential equations on meshes that need not conform to domain boundaries or interfaces. This talk gives an overview of the basic ideas for problems posed in bulk domains, on embedded surfaces, and on mixed-dimensional domains, coupling components of different dimensions.

We introduce the main ingredients of CutFEM discretizations, including the treatment of boundary and interface conditions, and outline a general analytical framework for establishing stability, error estimates, and bounds on the condition number. A central theme is robustness with respect to how the geometry intersects the background mesh. We discuss both weak stabilization through ghost penalties and strong stabilization through discrete extension, highlighting their principles and connections.

Several examples illustrate the methodology across different geometric settings, including applications to industrial CAD models. These examples demonstrate how CutFEM combines flexibility in geometric representation with accurate and robust numerical approximation.