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1 results

  • A Least-Squares/Fictitious Domain Method for Linear Elliptic Problems with Robin Boundary Conditions

  • Roland Glowinski, Qiaolin He
  • Journal:
    Communications in Computational Physics / Volume 9 / Issue 3 / March 2011
    Published online by Cambridge University Press:
    20 August 2015, pp. 587-606
    Print publication:
    March 2011

  • In this article, we discuss a least-squares/fictitious domain method for the solution of linear elliptic boundary value problems with Robin boundary conditions. Let Ω and ω be two bounded domains of Rd such that ω̅⊂Ω. For a linear elliptic problem in Ω\ω̅ with Robin boundary condition on the boundary ϒ of ω, our goal here is to develop a fictitious domain method where one solves a variant of the original problem on the full Ω, followed by a well-chosen correction over ω. This method is of the virtual control type and relies on a least-squares formulation making the problem solvable by a conjugate gradient algorithm operating in a well chosen control space. Numerical results obtained when applying our method to the solution of two-dimensional elliptic and parabolic problems are given; they suggest optimal order of convergence.