### Abstract

An optimization-based domain decomposition method for stochastic elliptic partial differential equations is presented. The main idea of the method is a constrained optimization problem for which the minimization of an appropriate functional forces the solutions on the two subdomains to agree on the interface; the constraints are the stochastic partial differential equations. The existence of optimal solutions for the stochastic optimal control problem is shown as is the convergence to the exact solution of the given problem. We prove the existence of a Lagrange multiplier and derive an optimality system from which solutions of the domain decomposition problem may be determined. Finite element approximations to the solutions of the optimality system are defined and analyzed with respect to both spatial and random parameter spaces. Then, the results of some numerical experiments are given to confirm theoretical error estimate results.

Original language | English |
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Pages (from-to) | 2262-2276 |

Number of pages | 15 |

Journal | Computers and Mathematics with Applications |

Volume | 68 |

Issue number | 12 |

DOIs | |

Publication status | Published - 2014 Dec 1 |

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### All Science Journal Classification (ASJC) codes

- Computational Theory and Mathematics
- Modelling and Simulation
- Computational Mathematics

### Cite this

*Computers and Mathematics with Applications*,

*68*(12), 2262-2276. https://doi.org/10.1016/j.camwa.2014.07.021

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*Computers and Mathematics with Applications*, vol. 68, no. 12, pp. 2262-2276. https://doi.org/10.1016/j.camwa.2014.07.021

**An optimization based domain decomposition method for PDEs with random inputs.** / Lee, Jangwoon; Lee, Jeehyun; Hwang, Yoongu.

Research output: Contribution to journal › Article

TY - JOUR

T1 - An optimization based domain decomposition method for PDEs with random inputs

AU - Lee, Jangwoon

AU - Lee, Jeehyun

AU - Hwang, Yoongu

PY - 2014/12/1

Y1 - 2014/12/1

N2 - An optimization-based domain decomposition method for stochastic elliptic partial differential equations is presented. The main idea of the method is a constrained optimization problem for which the minimization of an appropriate functional forces the solutions on the two subdomains to agree on the interface; the constraints are the stochastic partial differential equations. The existence of optimal solutions for the stochastic optimal control problem is shown as is the convergence to the exact solution of the given problem. We prove the existence of a Lagrange multiplier and derive an optimality system from which solutions of the domain decomposition problem may be determined. Finite element approximations to the solutions of the optimality system are defined and analyzed with respect to both spatial and random parameter spaces. Then, the results of some numerical experiments are given to confirm theoretical error estimate results.

AB - An optimization-based domain decomposition method for stochastic elliptic partial differential equations is presented. The main idea of the method is a constrained optimization problem for which the minimization of an appropriate functional forces the solutions on the two subdomains to agree on the interface; the constraints are the stochastic partial differential equations. The existence of optimal solutions for the stochastic optimal control problem is shown as is the convergence to the exact solution of the given problem. We prove the existence of a Lagrange multiplier and derive an optimality system from which solutions of the domain decomposition problem may be determined. Finite element approximations to the solutions of the optimality system are defined and analyzed with respect to both spatial and random parameter spaces. Then, the results of some numerical experiments are given to confirm theoretical error estimate results.

UR - http://www.scopus.com/inward/record.url?scp=84919427270&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84919427270&partnerID=8YFLogxK

U2 - 10.1016/j.camwa.2014.07.021

DO - 10.1016/j.camwa.2014.07.021

M3 - Article

VL - 68

SP - 2262

EP - 2276

JO - Computers and Mathematics with Applications

JF - Computers and Mathematics with Applications

SN - 0898-1221

IS - 12

ER -