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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)
  • Received : 2015.09.26
  • Accepted : 2015.12.13
  • Published : 2015.12.25

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.

Acknowledgement

Supported by : National Research Foundation of Korea (NRF)

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