Abstract
We present a unified framework based on potential and flux reconstruction for guaranteed and efficient a posteriori error estimation. We consider as model problems the Laplace equation, the singularly perturbed convection-diffusion-reaction equation, and the heat equation. The analysis is performed for a wide class of space discretization schemes. Three simple conditions need to be verified, which we do for cell- and vertex-centered finite volumes for all model problems.
MSC2010: 65M08, 65M15, 65M50, 65N08, 65N15, 65N50
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Acknowledgements
This work was partly supported by the Groupement MoMaS (PACEN/ CNRS, ANDRA, BRGM, CEA, EdF, IRSN).
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Ern, A., Vohralı́k, M. (2011). A Unified Framework for a posteriori Error Estimation in Elliptic and Parabolic Problems with Application to Finite Volumes. In: Fořt, J., Fürst, J., Halama, J., Herbin, R., Hubert, F. (eds) Finite Volumes for Complex Applications VI Problems & Perspectives. Springer Proceedings in Mathematics, vol 4. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20671-9_85
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DOI: https://doi.org/10.1007/978-3-642-20671-9_85
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