On a boundary control approach to domain embedding methods

In this paper, we propose a domain embedding method associated with an opti mal boundary control problem with boundary observations to solve elliptic p roblems. We prove that the optimal boundary control problem has a unique so lution if the controls are taken in a finite dimensional subspace of the sp ace of the boundary conditions on the auxiliary domain. Using a controllability theorem due to J. L. Lions, we prove that the solut ions of Dirichlet ( or Neumann) problems can be approximated within any pre scribed error, however small, by solutions of Dirichlet ( or Neumann) probl ems on the auxiliary domain taking an appropriate subspace for such an opti mal control problem. We also prove that the results obtained for the interi or problems hold for the exterior problems. Some numerical examples are giv en for both the interior and the exterior Dirichlet problems.