The stationary Boussinesq problem under singular forcing
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(,), 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 ∈ A1, 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 and local efficiency.
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