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http://dx.doi.org/10.12941/jksiam.2015.19.387

THE h × p FINITE ELEMENT METHOD FOR OPTIMAL CONTROL PROBLEMS CONSTRAINED BY STOCHASTIC ELLIPTIC PDES  

LEE, HYUNG-CHUN (DEPARTMENT OF MATHEMATICS, AJOU UNIVERSITY)
LEE, GWOON (DEPARTMENT OF MATHEMATICS, UNIVERSITY OF MARY WASHINGTON)
Publication Information
Journal of the Korean Society for Industrial and Applied Mathematics / v.19, no.4, 2015 , pp. 387-407 More about this Journal
Abstract
This paper analyzes the $h{\times}p$ version of the finite element method for optimal control problems constrained by elliptic partial differential equations with random inputs. The main result is that the $h{\times}p$ error bound for the control problems subject to stochastic partial differential equations leads to an exponential rate of convergence with respect to p as for the corresponding direct problems. Numerical examples are used to confirm the theoretical results.
Keywords
$h{\times}p$ version; finite element method; optimal control; stochastic elliptic equation; Karhunen-$Lo\grave{e}ve$ expansion; error estimates;
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