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

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