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

Abstract

This paper analyzes the h 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 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.