|Title:|| An optimal adaptive Fictitious Domain Method|
|Date:|| Wednesday 3rd January 2018|
|Author(s) :|| Berrone, S.; Bonito, A.; Stevenson, R.; Verani, M.|
|Abstract:|| We consider a Fictitious Domain formulation of an elliptic partial differential equation and approximate the resulting saddle-point system using an inexact preconditioned Uzawa iterative algorithm.
Each iteration entails the approximation of an elliptic problems performed using adaptive finite element methods. We prove that the overall method converges with the best possible rate and illustrate numerically our theoretical findings.|