### Abstract

In this article, we consider a guaranteed error estimate procedure for solutions to linear two-point boundary value problems. 'Guaranteed' error estimate is rigorous, i.e. it takes into account every error such as the discretization error and the rounding error when solving the problems. It also enables us to prove the existence and the uniqueness of the exact solution. We define the solution operator to bound the guaranteed error. In order to get an approximate solution, the finite element method is used. The original problem is transformed into an operator equation. There are two main points in our proposal method. One is to compute the inverse operator estimation. This estimation is obtained by Theorem1. The other is to get the residual of the operator equation. We lead the estimation of the residual by a standard norm estimation. Finally, some numerical results are presented.

Original language | English |
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Title of host publication | Asia Simulation Conference 2009, JSST 2009 |

Publisher | Japan Society for Simulation Technology, JSST |

Publication status | Published - 2009 |

Event | Asia Simulation Conference 2009, JSST 2009 - Shiga Duration: 2009 Oct 7 → 2009 Oct 9 |

### Other

Other | Asia Simulation Conference 2009, JSST 2009 |
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City | Shiga |

Period | 09/10/7 → 09/10/9 |

### Fingerprint

### Keywords

- Finite element method
- Guaranteed error estimate
- Two-point boundary value problem

### ASJC Scopus subject areas

- Modelling and Simulation

### Cite this

*Asia Simulation Conference 2009, JSST 2009*Japan Society for Simulation Technology, JSST.

**Guaranteed error estimate for solutions to linear two-point boundary value problems with FEM.** / Takayasu, Akitoshi; Oishi, Shinichi; Kubo, Takayuki.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Asia Simulation Conference 2009, JSST 2009.*Japan Society for Simulation Technology, JSST, Asia Simulation Conference 2009, JSST 2009, Shiga, 09/10/7.

}

TY - GEN

T1 - Guaranteed error estimate for solutions to linear two-point boundary value problems with FEM

AU - Takayasu, Akitoshi

AU - Oishi, Shinichi

AU - Kubo, Takayuki

PY - 2009

Y1 - 2009

N2 - In this article, we consider a guaranteed error estimate procedure for solutions to linear two-point boundary value problems. 'Guaranteed' error estimate is rigorous, i.e. it takes into account every error such as the discretization error and the rounding error when solving the problems. It also enables us to prove the existence and the uniqueness of the exact solution. We define the solution operator to bound the guaranteed error. In order to get an approximate solution, the finite element method is used. The original problem is transformed into an operator equation. There are two main points in our proposal method. One is to compute the inverse operator estimation. This estimation is obtained by Theorem1. The other is to get the residual of the operator equation. We lead the estimation of the residual by a standard norm estimation. Finally, some numerical results are presented.

AB - In this article, we consider a guaranteed error estimate procedure for solutions to linear two-point boundary value problems. 'Guaranteed' error estimate is rigorous, i.e. it takes into account every error such as the discretization error and the rounding error when solving the problems. It also enables us to prove the existence and the uniqueness of the exact solution. We define the solution operator to bound the guaranteed error. In order to get an approximate solution, the finite element method is used. The original problem is transformed into an operator equation. There are two main points in our proposal method. One is to compute the inverse operator estimation. This estimation is obtained by Theorem1. The other is to get the residual of the operator equation. We lead the estimation of the residual by a standard norm estimation. Finally, some numerical results are presented.

KW - Finite element method

KW - Guaranteed error estimate

KW - Two-point boundary value problem

UR - http://www.scopus.com/inward/record.url?scp=84903838644&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84903838644&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:84903838644

BT - Asia Simulation Conference 2009, JSST 2009

PB - Japan Society for Simulation Technology, JSST

ER -