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Hirpho, Mohammed

Numerical solution of the heat transfer equation coupled with the Darcy flow using the finite element method. (English) Zbl 1502.65123

Abstr. Appl. Anal. 2022, Article ID 5108445, 9 p. (2022).
Summary: 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.

MSC:

65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
35K05 Heat equation
80M20 Finite difference methods applied to problems in thermodynamics and heat transfer

Keywords:

finite element approach; heat transfer equation; Darcy flow; Picard-Lindelöf theorem

Software:

Matlab
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References:

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