Abstract
We derive a posteriori error estimates for the discretization of the unsteady linear convection–diffusion–reaction equation approximated with the cell-centered finite volume method in space and the backward Euler scheme in time. The estimates are based on a locally postprocessed approximate solution preserving the conservative fluxes and are established in the energy norm. We propose an adaptive algorithm which ensures the control of the total error with respect to a user-defined relative precision and refines the meshes adaptively while equilibrating the time and space contributions to the error. Numerical experiments illustrate the theory.
MSC2010: 65N15, 76M12, 76S05
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Acknowledgements
Nancy Chalhoub was supported by a joint fellowship from Ecole des Ponts ParisTech and CNRS Lebanon.
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Chalhoub, N., Ern, A., Sayah, T., Vohralı́k, M. (2011). A Posteriori Error Estimates for Unsteady Convection–Diffusion–Reaction Problems and the Finite Volume Method. 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_23
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DOI: https://doi.org/10.1007/978-3-642-20671-9_23
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