@article{17594,
  author = {C{\'e}cile Daversin-Catty and Chris Richardson and Ada Ellingsrud and Marie Rognes},
  title = {Abstractions and Automated Algorithms for Mixed Domain Finite Element Methods},
  abstract = {Mixed dimensional partial differential equations (PDEs) are equations coupling unknown fields defined over domains of differing topological dimension. Such equations naturally arise in a wide range of scientific fields including geology, physiology, biology, and fracture mechanics. Mixed dimensional PDEs are also commonly encountered when imposing non-standard conditions over a subspace of lower dimension, e.g., through a Lagrange multiplier. In this article, we present general abstractions and algorithms for finite element discretizations of mixed domain and mixed dimensional PDEs of codimension up to one (i.e., nD-mD with |n-m|},
  year = {2021},
  journal = {ACM Transactions on Mathematical Software},
  volume = {47},
  number = {4},
  publisher = {Association for Computing Machinery},
  doi = {10.1145/3471138},
}