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A posteriori error analysis for a continuous space-time finite element method for a hyperbolic integro-differential equation

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Abstract

An integro-differential equation of hyperbolic type, with mixed boundary conditions, is considered. A continuous space-time finite element method of degree one is formulated. A posteriori error representations based on space-time cells is presented such that it can be used for adaptive strategies based on dual weighted residual methods. A posteriori error estimates based on weighted global projections and local projections are also proved.

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Acknowledgements

I would like thank Prof. Stig Larsson for helpful discussion and constructive comments.

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Authors and Affiliations

  1. Department of Mathematics, University of Kurdistan, P.O. Box 416, Sanandaj, Iran

    Fardin Saedpanah

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  1. Fardin Saedpanah
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Correspondence to Fardin Saedpanah.

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Communicated by Ragnar Winther.

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Saedpanah, F. A posteriori error analysis for a continuous space-time finite element method for a hyperbolic integro-differential equation. Bit Numer Math 53, 689–716 (2013). https://doi.org/10.1007/s10543-013-0424-6

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  • DOI: https://doi.org/10.1007/s10543-013-0424-6

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