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An optimal error bound for a finite element approximation of spatially extended predator-prey interaction model

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Abstract

In this paper, we study a nonlinear in time finite element discretization of a spatially extended predator-prey interaction model. Assuming more regularity on the initial data and using the approach in Nochetto et al. (Commun. Pure Appl. Math. 53, 525–589 2000) for analyzing the time discretization error in the backward Euler method, we improve on the error bound derived in Garvie and Trenchea (Numer. Math. 107, 641–667 2007). We also present some numerical experiments to illustrate the improved error bound.

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Acknowledgments

The authors acknowledge the deanship of scientific research at King Faisal University for the financial support. We also thank the reviewers for their useful comments that contributed to improve our paper.

Funding

This work is supported by deanship of scientific research at King Faisal University under nasher track (Grant No. 186247).

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Faculty of Sciences, King Faisal University, P.O.Box 400, Alahsa, 31982, Kingdom of Saudi Arabia

    Ahmed A. Al Ghafli & Hassan J. Al Salman

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  1. Ahmed A. Al Ghafli
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  2. Hassan J. Al Salman
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Correspondence to Ahmed A. Al Ghafli.

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Al Ghafli, A.A., Al Salman, H.J. An optimal error bound for a finite element approximation of spatially extended predator-prey interaction model. Numer Algor 85, 209–229 (2020). https://doi.org/10.1007/s11075-019-00810-x

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  • DOI: https://doi.org/10.1007/s11075-019-00810-x

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