TY - CONF

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

AU - Takayasu, Akitoshi

AU - Oishi, Shin'ichi

AU - Kubo, Takayuki

PY - 2009/1/1

Y1 - 2009/1/1

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

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M3 - Paper

AN - SCOPUS:84903838644

T2 - Asia Simulation Conference 2009, JSST 2009

Y2 - 7 October 2009 through 9 October 2009

ER -