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Inverse Problems and Large-Scale Computations pp 57–68Cite as

A Posteriori Estimates for Errors of Functionals on Finite Volume Approximations to Solutions of Elliptic Boundary-Value Problems

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Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 52))

Abstract

This paper describes the extension of recent methods for a posteriori error estimation such as dual-weighted residual methods to node-centered finite volume discretizations of second-order elliptic boundary-value problems including upwind discretizations. It is shown how different sources of errors, in particular modeling errors and discretization errors, can be estimated with respect to a user-defined output functional.

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Acknowledgements

The author gratefully acknowledges support from the Visby Program of the Swedish Institute.

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Authors and Affiliations

  1. Institut für Mathematik, Technische Universität Clausthal, Erzstr. 1, 38678, Clausthal-Zellerfeld, Federal Republic of Germany

    Lutz Angermann

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  1. Lutz Angermann
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Correspondence to Lutz Angermann .

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Editors and Affiliations

  1. Department of Mathematical Sciences, Chalmers University of Technology Gothenburg University, Gothenburg, Sweden

    Larisa Beilina

  2. Karlstad University, Karlstad, Sweden

    Yury V. Shestopalov

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Angermann, L. (2013). A Posteriori Estimates for Errors of Functionals on Finite Volume Approximations to Solutions of Elliptic Boundary-Value Problems. In: Beilina, L., Shestopalov, Y. (eds) Inverse Problems and Large-Scale Computations. Springer Proceedings in Mathematics & Statistics, vol 52. Springer, Cham. https://doi.org/10.1007/978-3-319-00660-4_5

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