An optimal adaptive Fictitious Domain Method
Numerical Analysis
2018-09-21 v2
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.
Cite
@article{arxiv.1712.09281,
title = {An optimal adaptive Fictitious Domain Method},
author = {Stefano Berrone and Andrea Bonito and Rob Stevenson and Marco Verani},
journal= {arXiv preprint arXiv:1712.09281},
year = {2018}
}