### ADAPTIVE FINITE ELEMENT APPROXIMATION FOR A CLASS OF PARAMETER ESTIMATION PROBLEMS

Karl Kunisch1, Wenbin Liu2, Yanzhen Chang3, Ningning Yan3, Ruo Li4

1. 1. Department of Mathematics, University of Graz, Austria;
2. KBS, University of Kent,Canterbury, CT2 7NF, England;
3. LSEC, Academy of Mathematics and Systems Science,Chinese Academy of Sciences, Beijing, China;
4. Department of Computational Mathematics, Peking University, China+H8
• Received:2009-03-09 Revised:1900-01-01 Online:2010-09-15 Published:2010-09-15

Karl Kunisch, Wenbin Liu, Yanzhen Chang, Ningning Yan, Ruo Li. ADAPTIVE FINITE ELEMENT APPROXIMATION FOR A CLASS OF PARAMETER ESTIMATION PROBLEMS[J]. Journal of Computational Mathematics, DOI: 10.4208/jcm.2009.10-m1016.

In this paper, we study adaptive finite element discretisation schemes for a class of parameter estimation problem. We propose to use adaptive multi-meshes in developing efficient algorithms for the estimation problem. We derive equivalent a posteriori error estimators for both the state and the control approximation, which particularly suit an adaptive multi-mesh finite element scheme. The error estimators are then implemented and tested with promising numerical results.

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