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Convergence of BDF2-Galerkin finite element scheme for cancer invasion model

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Abstract

This article aims to determine the convergence and error bounds for the fully discrete solutions of the cancer invasion model using two-step backward difference scheme (BDF2) in time and Galerkin finite element approximation in space. The existence and uniqueness of a solution is affirmed. We establish error estimates with optimal order convergence rates for full discretization. Finally, some numerical tests are used to authenticate the scheme’s competency and accuracy.

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Authors and Affiliations

  1. Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Chennai, India

    S. Angelin Shena, J. Manimaran & K. Sethukumarasamy

  2. Department of Applied Sciences, National Institute of Technology Goa, Cuncolim, Goa, India

    L. Shangerganesh

Authors
  1. S. Angelin Shena
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  2. J. Manimaran
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  3. K. Sethukumarasamy
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  4. L. Shangerganesh
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Correspondence to J. Manimaran.

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Angelin Shena, S., Manimaran, J., Sethukumarasamy, K. et al. Convergence of BDF2-Galerkin finite element scheme for cancer invasion model. Eur. Phys. J. Spec. Top. (2024). https://doi.org/10.1140/epjs/s11734-024-01272-6

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  • DOI: https://doi.org/10.1140/epjs/s11734-024-01272-6

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