Abstract

The purpose of this work is the design and analysis of a posteriori error estimators for low-order stabilized finite element approximations of a generalized Boussinesq problem. We consider standard stabilization procedures over conforming finite element spaces and a nonconforming one that delivers a divergence-free discrete velocity field. The analysis, that is valid for two and three-dimensional domains, relies on a smallness assumption on the solution and is based on a technique that involves the Ritz projection of the residuals. The devised a posteriori error estimators are proven to be globally reliable and locally efficient. Three dimensional numerical experiments reveal a competitive performance of adaptive procedures driven by the designed a posteriori error estimators. (C) 2019 Elsevier B.V. All rights reserved.