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Convergence analysis of a spectral numerical method for a peridynamic formulation of Richards’ equation

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  • Difonzo, Fabio V.
  • Pellegrino, Sabrina F.

Abstract

We study the implementation of a Chebyshev spectral method with forward Euler integrator proposed in Berardi et al.(2023) to investigate a peridynamic nonlocal formulation of Richards’ equation. We prove the convergence of the fully-discretization of the model showing the existence and uniqueness of a solution to the weak formulation of the method by using the compactness properties of the approximated solution and exploiting the stability of the numerical scheme. We further support our results through numerical simulations, using initial conditions with different order of smoothness, showing reliability and robustness of the theoretical findings presented in the paper.

Suggested Citation

  • Difonzo, Fabio V. & Pellegrino, Sabrina F., 2024. "Convergence analysis of a spectral numerical method for a peridynamic formulation of Richards’ equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 223(C), pages 219-228.
    • Handle: RePEc:eee:matcom:v:223:y:2024:i:c:p:219-228
    DOI: 10.1016/j.matcom.2024.04.007
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    1. Wu, Xun & Zuo, Qiang & Shi, Jianchu & Wang, Lichun & Xue, Xuzhang & Ben-Gal, Alon, 2020. "Introducing water stress hysteresis to the Feddes empirical macroscopic root water uptake model," Agricultural Water Management, Elsevier, vol. 240(C).
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