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A POSTERIORI ERROR ESTIMATES FOR THE TWO-STEP BACKWARD DIFFERENTIATION FORMULA METHOD FOR PARABOLIC EQUATIONS

AKRIVIS, GEORGIOS ; CHATZIPANTELIDIS, PANAGIOTIS

SIAM journal on numerical analysis, 2010-01, Vol.48 (1), p.109-132 [Periódico revisado por pares]

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Título:
A POSTERIORI ERROR ESTIMATES FOR THE TWO-STEP BACKWARD DIFFERENTIATION FORMULA METHOD FOR PARABOLIC EQUATIONS
Autor: AKRIVIS, GEORGIOS ; CHATZIPANTELIDIS, PANAGIOTIS
Assuntos: A posteriori knowledge ; Approximation ; Cauchy problem ; Differentiation ; Discretization ; Error analysis ; Error rates ; Errors ; Estimates ; Estimation methods ; Estimators ; Eulers method ; Linear equations ; Mathematical analysis ; Mathematical differentiation ; Mathematical models ; Optimization ; Studies
É parte de: SIAM journal on numerical analysis, 2010-01, Vol.48 (1), p.109-132
Notas: ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
Descrição: We derive optimal order residual-based a posteriori error estimates for time discretizations by the two-step backward differentiation formula (BDF) method for linear parabolic equations. Appropriate reconstructions of the approximate solution play a key role in the analysis. To utilize the BDF method we employ one step by both the trapezoidal method or the backward Euler scheme. Our a posteriori error estimates are of optimal order for the former choice and suboptimal for the latter. Simple numerical experiments illustrate this behavior.
Editor: Philadelphia: Society for Industrial and Applied Mathematics
Idioma: Inglês

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