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A Stochastic Galerkin Method for Stochastic Control Problems

Published online by Cambridge University Press:  03 June 2015

Hyung-Chun Lee  and
Jangwoon Lee
Hyung-Chun Lee*
Affiliation:
Department of Mathematics, Ajou University, Suwon, Korea 443-749
Jangwoon Lee*
Affiliation:
Department of Mathematics, University of Mary Washington, Fredericksburg, VA 22401, USA
*
Corresponding author.Email:llee3@umw.edu
Email:hclee@ajou.ac.kr
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Abstract

In an interdisciplinary field on mathematics and physics, we examine a physical problem, fluid flow in porous media, which is represented by a stochastic partial differential equation (SPDE). We first give a priori error estimates for the solutions to an optimization problem constrained by the physical model under lower regularity assumptions than the literature. We then use the concept of Galerkin finite element methods to establish a new numerical algorithm to give approximations for our stochastic optimal physical problem. Finally, we develop original computer programs based on the algorithm and use several numerical examples of various situations to see how well our solver works by comparing its outputs to the priori error estimates.

Keywords

65M5565N30Stochastic Galerkin methodsstochastic partial differential equationdistributed controlfinite element methods
Type
Research Article
Information
Communications in Computational Physics , Volume 14 , Issue 1 , July 2013 , pp. 77 - 106
Copyright
Copyright © Global Science Press Limited 2013

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