A Least-Squares/Fictitious Domain Method for Linear Elliptic Problems with Robin Boundary Conditions (Communications in Computational Physics, 2011)
In this article, we discuss a least-squares/fictitious domain method for thesolution of linear elliptic boundary value problems with Robin boundary conditions.Let Ω and ω be two bounded domains of Rd such that ω⊂Ω. For a linear elliptic problemin Ω\ω with Robin boundary condition on the boundary γ of ω, our goal here is todevelop a fictitious domain method where one solves a variant of the original problemon the full Ω, followed by a well-chosen correction over ω. This method is of the virtualcontrol type and relies on a least-squares formulation making the problem solvable bya conjugate gradient algorithm operating in a well chosen control space. Numerical resultsobtained when applying our method to the solution of two-dimensional ellipticand parabolic problems are given; they suggest optimal order of convergence.