Abstract

In Lipschitz two-and three-dimensional domains, we study the existence for the so-called Boussinesq model of thermally driven convection under singular forcing. By singular we mean that the heat source is allowed to belong to H-1(, ω), where is a weight in the Muckenhoupt class A2 that is regular near the boundary. We propose a finite element scheme and, under the assumption that the domain is convex and-1 A 1, show its convergence. In the case that the thermal diffusion and viscosity are constants, we propose an a posteriori error estimator and show its reliability. We also explore efficiency estimates.