Darcy's problem coupled with the heat equation under singular forcing: analysis and discretization
Numerical Analysis
2022-08-30 v1 Numerical Analysis
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.
Cite
@article{arxiv.2208.12887,
title = {Darcy's problem coupled with the heat equation under singular forcing: analysis and discretization},
author = {A. Allendes and G. Campaña and F. Fuica and E. Otarola},
journal= {arXiv preprint arXiv:2208.12887},
year = {2022}
}