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Identification of matrix parameters in elliptic PDEs

by Deckelnick, K; Hinze, M..

Series: 2011-03, Preprints

49J20 Optimal control problems involving partial differential equations
49K20 Problems involving partial differential equations

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.

Parameter identification, elliptic optimal control problem, control constraints, H-convergence, variational discretization