J. Comp. Math., 28 (2010), pp. 645-675.


ADAPTIVE FINITE ELEMENT APPROXIMATION FOR A CLASS OF PARAMETER ESTIMATION PROBLEMS

Karl Kunisch 1, Wenbin Liu 2, Yanzhen Chang 3, Ningning Yan 3, Ruo Li 4

1 Department of Mathematics, University of Graz, Austria
2 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

Received 2009-3-9 Accepted 2009-6-6
Available online 2010-5-1
doi:10.4208/jcm.2009.10-m1016

Abstract

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.

Key words: Parameter estimation, Finite element approximation, Adaptive finite element methods, A posteriori error estimate

AMS subject classifications: 49J20, 65N30


Email: karl.kunisch@uni-graz.at, w.b.liu@kent.ac.uk, ynn@amss.ac.cn, rli@math.pku.edu.cn
 

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