Publication Cover
Applicable Analysis
An International Journal
Volume 92, 2013 - Issue 7
47
Views
1
CrossRef citations to date
0
Altmetric
Articles

Adaptive error control during gradient search for an elliptic optimization problem

&
Pages 1434-1448 | Received 29 Apr 2011, Accepted 02 Apr 2012, Published online: 22 May 2012
 

Abstract

In this article we describe a cost effective adaptive procedure for optimization of a quantity of interest of a solution of an elliptic problem with respect to parameters in the data, using a gradient search approach. The numerical error in both the quantity of interest and the computed gradient may affect the progression of the search algorithm, while the errors generally change at each step during the search algorithm. We address this by using an accurate a posteriori estimate for the error in a quantity of interest that indicates the effect of error on the computed gradient and so provides a measure for how to refine the discretization as the search proceeds. Specifically, we devise an adaptive algorithm to refine and unrefine the finite element mesh at each step in the search algorithm. We give basic examples and apply this technique to a model of a healing wound.

AMS Subject Classifications:

Acknowledgements

Estep's work is supported in part by the Defense Threat Reduction Agency (HDTRA1-09-1-0036), Department of Energy (DE-FG02-04ER25620, DE-FG02-05ER25699, DE-FC02-07ER54909, DE-SC0001724, DE-SC0005304, INL00120133), Lawrence Livermore National Laboratory (B573139, B584647, B590495), the National Aeronautics and Space Administration (NNG04GH63G), the National Institutes of Health (5R01GM096192-02), the National Science Foundation (DMS-0107832, DMS-0715135, DGE-0221595003, MSPA-CSE-0434354, ECCS-0700559, DMS-1016268, DMS-FRG-1065046) and Idaho National Laboratory (00069249, 00115474). Lee's work is supported in part by the Department of Energy (DE-FG02-05ER25699) and the National Science Foundation (DMS-0107832).

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.