Open Collections

Unfitted finite element simulations based on cell aggregation

Banff International Research Station for Mathematical Innovation and Discovery

In this talk, we will explore cell aggregation techniques for finite element numerical approximations with unfitted meshes, when using conforming spaces. We will present and analyze the method, show how it solves the small cut cell problem, and discuss its numerical implementation. We have combined this strategy with octree meshes to deal with large scale problems. We will also show parallel simulations with unfitted methods based on aggregation, and comment on the linear solver and octree handling steps. Finally, we will consider the Stokes problem, and analyze the well-posedness of the aggregated approach when using mixed finite element methods. It will motivate the introduction of a minimal stabilization and the use of new types of extension operators in the aggregated method.

Mathematics; Numerical analysis; Partial differential equations

video/mp4

Author affiliation: Universitat Politècnica de Catalunya

2019-03-16

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/68813

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/