A local projection stabilized method for fictitious domains

TL;DR

This paper introduces a local projection stabilization technique for fictitious domain problems, enhancing stability and convergence through a fluctuation term, supported by theoretical proofs and numerical experiments.

Contribution

It presents a novel local projection stabilization method that improves the stability of fictitious domain formulations with rigorous analysis and numerical validation.

Findings

Stability of the proposed method is theoretically proven.

Convergence of the method is established.

Numerical experiments confirm the theoretical results.

Abstract

In this work a local projection stabilization method is proposed to solve a fictitious domain problem. The method adds a suitable fluctuation term to the formulation thus rendering the natural space for the Lagrange multiplier stable. Stability and convergence are proved and these results are illustrated by a numerical experiment.