Volume 14, Issue 1
A Stochastic Galerkin Method for Stochastic Control Problems

Hyung-Chun Lee & Jangwoon Lee

Commun. Comput. Phys., 14 (2013), pp. 77-106.

Published online: 2014-07

Preview Full PDF 340 849
Export citation
  • 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

  • AMS Subject Headings

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • References
  • Hide All
    View All

  • BibTex
  • RIS
  • TXT
@Article{CiCP-14-77, author = {Hyung-Chun Lee and Jangwoon Lee}, title = {A Stochastic Galerkin Method for Stochastic Control Problems}, journal = {Communications in Computational Physics}, year = {2014}, volume = {14}, number = {1}, pages = {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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.241011.150612a}, url = {http://global-sci.org/intro/article_detail/cicp/7151.html} }
TY - JOUR T1 - A Stochastic Galerkin Method for Stochastic Control Problems AU - Hyung-Chun Lee & Jangwoon Lee JO - Communications in Computational Physics VL - 1 SP - 77 EP - 106 PY - 2014 DA - 2014/07 SN - 14 DO - http://dor.org/10.4208/cicp.241011.150612a UR - https://global-sci.org/intro/cicp/7151.html KW - AB -

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.

Hyung-Chun Lee & Jangwoon Lee. (1970). A Stochastic Galerkin Method for Stochastic Control Problems. Communications in Computational Physics. 14 (1). 77-106. doi:10.4208/cicp.241011.150612a
Copy to clipboard
The citation has been copied to your clipboard