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Numerical Solution of the Heat Transfer Equation Coupled with the Darcy Flow Using the Finite Element Method

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  • Mohammed Hirpho
  • Chun Gang Zhu

Abstract

The finite element approach was utilized in this study to solve numerically the two-dimensional time-dependent heat transfer equation coupled with the Darcy flow. The Picard-Lindelöf Theorem was used to prove the existence and uniqueness of the solution. The prior and posterior error estimates are then derived for the numerical scheme. Numerical examples were provided to show the effectiveness of the theoretical results. The essential code development in this study was done using MATLAB computer simulation.

Suggested Citation

  • Mohammed Hirpho & Chun Gang Zhu, 2022. "Numerical Solution of the Heat Transfer Equation Coupled with the Darcy Flow Using the Finite Element Method," Abstract and Applied Analysis, Hindawi, vol. 2022, pages 1-9, April.
    • Handle: RePEc:hin:jnlaaa:5108445
    DOI: 10.1155/2022/5108445
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