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Title
Error estimation based on locally weighted defect for boundary value problems in second order ordinary differential equations
AuthorAuzinger, Winfried
ParticipantsKoch, Othmar ; Saboor Bagherzadeh, Amir
Published in
BIT Numerical Mathematics, 2014, Vol. 54, Issue 4, page 873-900
PublishedSpringer, 2014
Edition
Accepted version
Annotation
The final publication is available at Springer via http://dx.doi.org/10.1007/s10543-014-0488-y.
LanguageEnglish
Document typeJournal Article
Keywords (EN)Second order boundary value problems / Collocation methods / Asymptotically correct a posteriori error estimates / Defect correction principle / Exact difference scheme / Supraconvergence
URNurn:nbn:at:at-ubtuw:3-1130 Persistent Identifier (URN)
DOI10.1007/s10543-014-0488-y 
Restriction-Information
 The work is publicly available
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Error estimation based on locally weighted defect for boundary value problems in second order ordinary differential equations [0.41 mb]
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Abstract (English)

We investigate efficient asymptotically correct a posteriori error estimates for the numerical approximation of two-point boundary value problems for second order ordinary differential equations by piecewise polynomial collocation methods. Our error indicators are based on the defect of the collocation solution with respect to an associated exact difference scheme and backsolving using a cheap, low order finite-difference scheme. We prove high asymptotical correctness of this error indicator and illustrate the theoretical analysis by numerical examples.

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