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Volume 28, Issue 5
Adaptive Finite Element Approximation for a Class of Parameter Estimation Problems

Karl Kunisch, Wenbin Liu, Yanzhen Chang, Ningning Yan & Ruo Li

DOI: 10.4208/jcm.2009.10-m1016

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

Published online: 2010-10

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  • 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.

  • Keywords

Parameter estimation, Finite element approximation, Adaptive finite element methods, A posteriori error estimate.

  • AMS Subject Headings

49J20, 65N30

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-28-645, author = {Karl Kunisch, Wenbin Liu, Yanzhen Chang, Ningning Yan and Ruo Li}, title = {Adaptive Finite Element Approximation for a Class of Parameter Estimation Problems}, journal = {Journal of Computational Mathematics}, year = {2010}, volume = {28}, number = {5}, pages = {645--675}, 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.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.2009.10-m1016}, url = {http://global-sci.org/intro/article_detail/jcm/8542.html} }
TY - JOUR T1 - Adaptive Finite Element Approximation for a Class of Parameter Estimation Problems AU - Karl Kunisch, Wenbin Liu, Yanzhen Chang, Ningning Yan & Ruo Li JO - Journal of Computational Mathematics VL - 5 SP - 645 EP - 675 PY - 2010 DA - 2010/10 SN - 28 DO - http://doi.org/10.4208/jcm.2009.10-m1016 UR - https://global-sci.org/intro/article_detail/jcm/8542.html KW - Parameter estimation, Finite element approximation, Adaptive finite element methods, A posteriori error estimate. AB -

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.

Karl Kunisch, Wenbin Liu, Yanzhen Chang, Ningning Yan and Ruo Li. (2010). Adaptive Finite Element Approximation for a Class of Parameter Estimation Problems. Journal of Computational Mathematics. 28 (5). 645-675. doi:10.4208/jcm.2009.10-m1016
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