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Distributed Control of the Stochastic Burgers Equation with Random Input Data

Part of: Incompressible viscous fluids Existence theories

Published online by Cambridge University Press:  27 January 2016

Hyung-Chun Lee  and
Yun Nam
Hyung-Chun Lee*
Affiliation:
Department of Mathematics, Ajou University, Suwon, Korea 16499
Yun Nam
Affiliation:
Department of Mathematics, Ajou University, Suwon, Korea 16499
*
*Corresponding author. Email addresses:hclee@ajou.ac.kr (H.-C. Lee), namy0727@ajou.ac.kr (Y. Nam)
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Abstract

We discuss a control problem involving a stochastic Burgers equation with a random diffusion coefficient. Numerical schemes are developed, involving the finite element method for the spatial discretisation and the sparse grid stochastic collocation method in the random parameter space. We also use these schemes to compute closed-loop suboptimal state feedback control. Several numerical experiments are performed, to demonstrate the efficiency and plausibility of our approximation methods for the stochastic Burgers equation and the related control problem.

Keywords

Finite element methodfeedback controlstochastic Burgers equationsparse grid collocation

MSC classification

Secondary: 49J20: Optimal control problems involving partial differential equations 76D05: Navier-Stokes equations
Type
Research Article
Information
East Asian Journal on Applied Mathematics , Volume 6 , Issue 1 , February 2016 , pp. 89 - 108
Copyright
Copyright © Global-Science Press 2016 

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