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

Akitoshi Takayasu, Shinichi Oishi, Takayuki Kubo

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    2 Citations (Scopus)

    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 languageEnglish
    Title of host publicationAsia Simulation Conference 2009, JSST 2009
    PublisherJapan Society for Simulation Technology, JSST
    Publication statusPublished - 2009
    EventAsia Simulation Conference 2009, JSST 2009 - Shiga
    Duration: 2009 Oct 72009 Oct 9

    Other

    OtherAsia Simulation Conference 2009, JSST 2009
    CityShiga
    Period09/10/709/10/9

    Fingerprint

    Two-point Boundary Value Problem
    Boundary value problems
    Error Estimates
    Finite element method
    Operator Equation
    Mathematical operators
    Discretization Error
    Rounding error
    Operator
    Approximate Solution
    Uniqueness
    Exact Solution
    Finite Element Method
    Norm
    Numerical Results

    Keywords

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

    ASJC Scopus subject areas

    • Modelling and Simulation

    Cite this

    Takayasu, A., Oishi, S., & Kubo, T. (2009). Guaranteed error estimate for solutions to linear two-point boundary value problems with FEM. In 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.

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

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Takayasu, A, Oishi, S & Kubo, T 2009, Guaranteed error estimate for solutions to linear two-point boundary value problems with FEM. in Asia Simulation Conference 2009, JSST 2009. Japan Society for Simulation Technology, JSST, Asia Simulation Conference 2009, JSST 2009, Shiga, 09/10/7.
    Takayasu A, Oishi S, Kubo T. Guaranteed error estimate for solutions to linear two-point boundary value problems with FEM. In Asia Simulation Conference 2009, JSST 2009. Japan Society for Simulation Technology, JSST. 2009
    Takayasu, Akitoshi ; Oishi, Shinichi ; Kubo, Takayuki. / Guaranteed error estimate for solutions to linear two-point boundary value problems with FEM. Asia Simulation Conference 2009, JSST 2009. Japan Society for Simulation Technology, JSST, 2009.
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