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A Stochastic Galerkin Method for Stochastic Control Problems

A Stochastic Galerkin Method for Stochastic Control Problems
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Year:    2013

Communications in Computational Physics, Vol. 14 (2013), Iss. 1 : pp. 77–106

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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cicp.241011.150612a

Communications in Computational Physics, Vol. 14 (2013), Iss. 1 : pp. 77–106

Published online:    2013-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    30

Keywords:   

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