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Local Error Estimates for the SUPG Method Applied to Evolutionary Convection–Reaction–Diffusion Equations

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Abstract

Local error estimates for the SUPG method applied to evolutionary convection–reaction–diffusion equations are considered. The steady case is reviewed and local error bounds are obtained for general order finite element methods. For the evolutionary problem, local bounds are obtained when the SUPG method is combined with the backward Euler scheme. The arguments used in the proof lead to estimates for the stabilization parameter that depend on the length on the time step. The numerical experiments show that local bounds seem to hold true both with a stabilization parameter depending only on the spatial mesh grid and with other time integrators.

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Acknowledgments

The authors would like to thank an anonymous referee for his or her valuable comments.

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Correspondence to Julia Novo.

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Javier de Frutos and Julia Novo: The research was supported by Spanish MICINN under Grants MTM2010-14919 and MTM2013-42538-P.

Bosco García-Archilla: The research was supported by Spanish MICINN under Grant MTM2012-31821.

Javier de Frutos acknowledges the support of European Cooperation in Science and Technology through COST Action IS1104.

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de Frutos, J., García-Archilla, B. & Novo, J. Local Error Estimates for the SUPG Method Applied to Evolutionary Convection–Reaction–Diffusion Equations. J Sci Comput 66, 528–554 (2016). https://doi.org/10.1007/s10915-015-0035-2

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  • DOI: https://doi.org/10.1007/s10915-015-0035-2

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