The aggregated unfitted finite element method for elliptic problems

Santiago Badia*, Francesc Verdugo, Alberto F. Martín

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

79 Citations (Scopus)


Unfitted finite element techniques are valuable tools in different applications where the generation of body-fitted meshes is difficult. However, these techniques are prone to severe ill conditioning problems that obstruct the efficient use of iterative Krylov methods and, in consequence, hindersthe practical usage of unfitted methods for realistic large scale applications. In this work, we present a technique that addresses such conditioning problems by constructing enhanced finite element spaces based on a cell aggregation technique. The presented method, called aggregated unfitted finite element method, is easy to implement, and can be used, in contrast to previous works, in Galerkin approximations of coercive problems with conforming Lagrangian finite element spaces. The mathematical analysis of the method states that the condition number of the resulting linear system matrix scales as in standard finite elements for body-fitted meshes, without being affected by small cut cells, and that the method leads to the optimal finite element convergence order. These theoretical results are confirmed with 2D and 3D numerical experiments.

Original languageEnglish
Pages (from-to)533-553
Number of pages21
JournalComputer Methods in Applied Mechanics and Engineering
Publication statusPublished - 1 Jul 2018
Externally publishedYes


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