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Error analysis of a fictitious domain method applied to a Dirichlet problem. (English) Zbl 0843.65076
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.

MSC:
65N15 Error bounds for boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations
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