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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 = {}, 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 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 & Ruo Li. (1970). 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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