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

Title & Authors
THE h × p FINITE ELEMENT METHOD FOR OPTIMAL CONTROL PROBLEMS CONSTRAINED BY STOCHASTIC ELLIPTIC PDES
LEE, HYUNG-CHUN; LEE, GWOON;

Abstract
This paper analyzes the $\small{h{\times}p}$ 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 $\small{h{\times}p}$ 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
$\small{h{\times}p}$ version;finite element method;optimal control;stochastic elliptic equation;Karhunen-$\small{Lo\grave{e}ve}$ expansion;error estimates;
Language
English
Cited by
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