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Titel
Error estimation based on locally weighted defect for boundary value problems in second order ordinary differential equations
VerfasserAuzinger, Winfried In der Gemeinsamen Normdatei der DNB nachschlagen
BeteiligteKoch, Othmar In der Gemeinsamen Normdatei der DNB nachschlagen ; Saboor Bagherzadeh, Amir
Erschienen in
BIT Numerical Mathematics, 2014, Jg. 54, H. 4, S. 873-900
ErschienenSpringer 2014
Ausgabe
Accepted version
SpracheEnglisch
DokumenttypAufsatz in einer Zeitschrift
Schlagwörter (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)
DOIdoi:10.1007/s10543-014-0488-y 
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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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Zusammenfassung (Englisch)

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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