@misc{17605,
  author = {C{\'e}cile Daversin-Catty and Joseph Dean and Marie Rognes and Garth Wells},
  title = {Mixed-Domain Coupled Finite Elements in FEniCSx},
  abstract = {Mixed-dimensional partial differential equations (PDEs) are equations coupling fields defined over distinct domains that may differ in topological dimension. Such PDEs naturally arise in a wide range of fields including geology, bio-medicine, and fracture mechanics. Mixed-dimensional models are also used to impose non-standard conditions through Lagrange multipliers. Finite element discretizations of such PDEs involve nested meshes of possibly heterogeneous topological dimension. The assembly of such systems is non-standard and non-trivial, and requires the design of both generic high level software abstractions and lower level algorithms. The FEniCS project aims at automating the numerical solution of PDE-based models using finite element methods. A core feature is a high-level domain-specific language for finite element spaces and variational forms, close to mathematical syntax. Lately, FEniCS gave way to its successor FEniCSx, including major improvements over the legacy library. An automated framework was developed in core FEniCS legacy libraries to address the challenges characterizing mixed-dimensional problems. These concepts were recently ported to FEniCSx, taking advantage of the underlying upgrades in the library features and design. This talk gives an overview of the abstractions and algorithms involved, and their implementation in the FEniCS project core libraries. The introduced features are illustrated by concrete applications in engineering and biomedicine.},
  year = {2023},
  journal = {SIAM CSE23 - Amsterdam, the Netherlands},
}