09-206 Larisa Beilina, Michael V. Klibanov and Mikhail Yu. Kokurin

Adaptivity with relaxation for ill-posed problems and global convergence for a coefficient inverse problem (775K, pdf) Nov 20, 09

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Abstract. A new framework of the Functional Analysis is developed for the adaptive FEM (adaptivity) for the Tikhonov regularization functional for ill-posed problems. As a result, the relaxation property for adaptive mesh refinements is established. An application to a multidimensional Coefficient Inverse Problem for a hyperbolic equation is discussed. This problem arises in the inverse scattering of acoustic and electromagnetic waves. First, a globally convergent numerical method provides a good approximation for the correct solution of this problem. Next, this approximation is enhanced via the subsequent application of the adaptivity. Analytical results are computationally verified

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