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Anisotropic a Posteriori Error Analysis for the Two-Step Backward Differentiation Formula for Parabolic Integro-Differential Equation

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Abstract

Residual-based anisotropic a posteriori error estimates are derived for the parabolic integro-differential equation (PIDE) with smooth kernel in two-dimensions. Based on \(C^0\)-conforming piecewise linear elements for spatial discretization, the fully discrete method is achieved after discretizing in time by a two-step backward difference (BDF-2) formula. Reconstruction technique is used to restore the optimal order convergence in temporal direction. Numerical results confirm our theoretical findings.

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Acknowledgements

The authors wish to thank the referees for their valuable suggestions which help to improve this paper. The second author would like to thank SERB, India for the financial support received [Grant Number SRG/2019/001973]. Further, the first and second authors acknowledge DST, New Delhi, India, for providing facilities through DST-FIST lab, Department of Mathematics, BITS-Pilani, Hyderabad Campus, where a part of this work has been done.

Funding

The authors have not disclosed any funding. The second author would like to thank SERB, India for the financial support received [Grant Number SRG/2019/001973].

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Authors and Affiliations

  1. Department of Mathematics, BITS Pilani Hyderabad campus, Hyderabad, 500078, India

    N Shravani & G Murali Mohan Reddy

  2. Department of Mathematics, Birla Institute of Technology & Science, Pilani, KK Birla Goa Campus, NH 17 B, Zuarinagar, Goa, 403726, India

    A. K. Pani

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  1. N Shravani
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  2. G Murali Mohan Reddy
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  3. A. K. Pani
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Correspondence to A. K. Pani.

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Shravani, N., Reddy, G.M.M. & Pani, A.K. Anisotropic a Posteriori Error Analysis for the Two-Step Backward Differentiation Formula for Parabolic Integro-Differential Equation. J Sci Comput 93, 26 (2022). https://doi.org/10.1007/s10915-022-01996-4

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  • DOI: https://doi.org/10.1007/s10915-022-01996-4

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