The h × p Finite Element Method for Optimal Control Problems Constrained by Stochastic Elliptic PDEs

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Journal of the Korean Society for Industrial and Applied Mathematics

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This paper analyzes the h X 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.


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The journal of the Korean Society for Industrial and Applied Mathematics(J-KSIAM) is published by the Korean Society for Industrial and Applied Mathematics(KSIAM). This aims to publish research articles that deal with scientific or engineering problems by using a variety of mathematical methods. Computational results demonstrating the effectiveness of the proposed techniques are also included.