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arXiv · 2208.12887

Darcy's problem coupled with the heat equation under singular forcing: analysis and discretization

A. Allendes·G. Campaña·F. Fuica·E. Otarola
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Abstract

We study the existence of solutions for Darcy's problem coupled with the heat equation under singular forcing; the right-hand side of the heat equation corresponds to a Dirac measure. The studied model allows thermal diffusion and viscosity depending on the temperature. We propose a finite element solution technique and analyze its convergence properties. In the case that the thermal diffusion is constant, we propose an a posteriori error estimator and investigate reliability and efficiency properties. We illustrate the theory with numerical examples.

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A. Allendes, G. Campaña, F. Fuica, E. Otarola. 2022-08-26. Darcy's problem coupled with the heat equation under singular forcing: analysis and discretization. https://arxiv.org/abs/2208.12887

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