In this article, new unfitted mixed finite elements are presented for elliptic interface problems with jump coefficients. Our model is based on a fictitious domain formulation with distributed Lagrange multiplier. The relevance of our investigations is better seen when applied to the framework of fluid-structure interaction problems. Two finite element schemes with piecewise constant Lagrange multiplier are proposed and their stability is proved theoretically. Numerical results compare the performance of those elements, confirming the theoretical proofs and verifying that the schemes converge with optimal rates.
|Original language||English (US)|
|Journal||Numerical Methods for Partial Differential Equations|
|State||Published - Aug 11 2023|
ASJC Scopus subject areas
- Computational Mathematics
- Applied Mathematics
- Numerical Analysis