caa a22 4500 378879855 CHVBK 20180305123429.0 cr unu---uuuuu 161128e20031215xx s 000 0 eng 10.1515/156939403322759660 doi (NATIONALLICENCE)gruyter-10.1515/156939403322759660 Beilina L. Department of Mathematics, Chalmers University of Technology, S-412 96 Göteborg, Sweden. E-mail: larisa@math.chalmers.se Adaptive hybrid finite element/difference methods: application to inverse elastic scattering [Elektronische Daten] [L. Beilina] We use an optimal control approach for solution of inverse problem for time-dependent scattering of elastic waves in , d = 2, 3 where we seek a density ρ and Lamé coefficients λ and μ which minimize the difference between computed and measured output data in a discrete L 2 norm. We solve the optimization problem by a quasi-Newton method, where in each step we compute the gradient by solving a forward and an adjoint elastic wave propagation problem. We develop a posteriori error estimator for the error in Lagrangian and apply it to solution of inverse problem for time-dependent scattering of elastic waves in , d = 2, 3. For implementation of the inverse problem we use an adaptive hybrid finite element/difference methods, where we combine the flexibility of finite elements and the efficiency of finite differences. We present computational results for three dimensional inverse scattering and use an adaptive mesh refinement algorithm based on an a posteriori error estimate, to improve the accuracy of the identification. Copyright 2003, Walter de Gruyter Journal of Inverse and Ill-posed Problems Walter de Gruyter 11/6(2003-12-15), 585-618 0928-0219 11:6<585 2003 11 jiip https://doi.org/10.1515/156939403322759660 text/html Onlinezugriff via DOI 1 research article jats NATIONALLICENCE 856 40 https://doi.org/10.1515/156939403322759660 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Beilina L. Department of Mathematics, Chalmers University of Technology, S-412 96 Göteborg, Sweden. E-mail: larisa@math.chalmers.se NATIONALLICENCE 773 0- Journal of Inverse and Ill-posed Problems Walter de Gruyter 11/6(2003-12-15), 585-618 0928-0219 11:6<585 2003 11 jiip CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-gruyter