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<p>The time-dependent Darcy system, when discretized in time using the implicit Euler scheme and in space using the spectral element method, can be efficiently solved using the penalty method. This approach allows the decoupling of the computations for velocity and pressure. We also derive a priori error estimates for the spectral element discretization of the time-dependent Darcy equations.</p>

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The Penalty resolution of the spectral element discretization of the time dependent Darcy equations

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年12月22日

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  • Nejmeddine Chorfi,
  • Mohamed Abdelwahed,
  • Henda Ouertani

摘要

The time-dependent Darcy system, when discretized in time using the implicit Euler scheme and in space using the spectral element method, can be efficiently solved using the penalty method. This approach allows the decoupling of the computations for velocity and pressure. We also derive a priori error estimates for the spectral element discretization of the time-dependent Darcy equations.