Series: 2011-03, Preprints
Abstract:
We consider the inverse problem of identifying the matrix-valued diffusion coefficient of an elliptic PDE from measurements with the help of techniques from PDE constrained optimization. We prove existence of solutions using the concept of H-convergence and employ variational discretization for the discrete approximation of solutions. Using a discrete version of H-convergence we are able to establish the strong convergence of the discrete solutions.
Keywords:
Parameter identification, elliptic optimal control problem, control constraints, H-convergence, variational discretization