An optimal adaptive Fictitious Domain Method
arXiv:1712.0928110 citations
Originality Synthesis-oriented
AI Analysis
Provides a theoretically optimal adaptive solver for fictitious domain methods, which is an incremental improvement in numerical PDE methodology.
The authors develop an adaptive fictitious domain method for elliptic PDEs, proving optimal convergence rates and validating them numerically.
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.