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Identification of matrix parameters in elliptic PDEs

Deckelnick K., Hinze M.

Control and Cybernetics

2011

Vol. 40, no 4

957-969

In the present work we treat the inverse problem of identifying the matrix-valued diffusion coefficient of an elliptic PDE from multiple interior 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. Finally we present some numerical results.