### 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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Publication status | Published - 2009 Jan 1 |

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

### Conference

Conference | Asia Simulation Conference 2009, JSST 2009 |
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Country | Japan |

City | Shiga |

Period | 09/10/7 → 09/10/9 |

### Keywords

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

### ASJC Scopus subject areas

- Modelling and Simulation

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## Cite this

*Guaranteed error estimate for solutions to linear two-point boundary value problems with FEM*. Paper presented at Asia Simulation Conference 2009, JSST 2009, Shiga, Japan.