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<p>This study introduces and thoroughly analyzes a novel mixed formulation for modeling seawater intrusion in confined aquifers, employing a sharp/diffuse interface approach. By reformulating the model in matrix form and incorporating an innovative variable, we extend our analysis from the stationary to the non-stationary regime, thereby establishing the well-posedness of the continuous problem. We then develop a semi-discrete mixed formulation and demonstrate the existence and uniqueness of its solution. Our rigorous error estimates, comparing the exact and semi-discrete solutions, confirm consistency with the stationary case, indicating that the error rates align in both the <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(L^\infty \)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>L</mi> <mi>∞</mi> </msup> </math></EquationSource> </InlineEquation> norm in time and the <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(L^2\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>L</mi> <mn>2</mn> </msup> </math></EquationSource> </InlineEquation> norm in space. This work not only advances the theoretical understanding of seawater intrusion dynamics but also provides a robust framework for practical applications in hydrological modeling.</p>

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Advancing seawater intrusion modeling: a semi-implicit mixed finite element method with sharp/diffuse interface approach

  • 期刊论文

  • 发表日期：

    2026年7月22日

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  • Ibtissam Medarhri,
  • Mohamed Farhloul,
  • Khalid Najib,
  • Abdelmalek Zine

摘要

This study introduces and thoroughly analyzes a novel mixed formulation for modeling seawater intrusion in confined aquifers, employing a sharp/diffuse interface approach. By reformulating the model in matrix form and incorporating an innovative variable, we extend our analysis from the stationary to the non-stationary regime, thereby establishing the well-posedness of the continuous problem. We then develop a semi-discrete mixed formulation and demonstrate the existence and uniqueness of its solution. Our rigorous error estimates, comparing the exact and semi-discrete solutions, confirm consistency with the stationary case, indicating that the error rates align in both the \(L^\infty \) L ∞ norm in time and the \(L^2\) L 2 norm in space. This work not only advances the theoretical understanding of seawater intrusion dynamics but also provides a robust framework for practical applications in hydrological modeling.