(untitled) (Advances in Applied Mathematics and Mechanics, 2018)
In this article, we discuss a modified least–squares fictitious domain method for the solution of linear elliptic boundary value problems with the third type of boundary conditions (Robin boundary conditions). Let Ω and ω be two bounded domains of R^d such that ω Ω. For a linear elliptic problem in Ωω with Robin boundary conditions on the boundary γ of ω, we accelerate the original least–squares fictitious domain method in Glowinski & He [1] and present a modified least–squares formulation. This method is still a virtual control type and relies on a least-squares formulation, which makes the problem solvable by a conjugate gradient algorithm operating in a well chosen control space. Numerical results show that our method costs much less iterations and the optimal order of convergence is obtained.