Error analysis of a fictitious domain method applied to a Dirichlet problem (Q1908888)

The purpose of this paper is to derive error estimates of a fictitious domain method with a Lagrange multiplier. The main goal is the proof of a uniform discrete inf-sup conditon via the construction of a suitable restriction operator. The nonlinear analysis is presented in the simplified case where the boundary is a polygon. This study is applied to solve a non-homogeneous elliptic Dirichlet problem with conforming finite elements of degree one on a regular grid.