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

Document Type

Article

Digital Object Identifier (DOI)

10.12941/jksiam.2015.19.387

Journal Title

Journal of the Korean Society for Industrial and Applied Mathematics

Publication Date

2015

Abstract

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.

Comments

This article is freely available on the web.

Additional issues can be found on the J-KSIAM website at: http://koreascience.or.kr/journal/E1TAAE.page.

Publisher Statement

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.

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