Dual-mixed finite element methods for the stationary Boussinesq problem. (October 2016)

• Record Type: Journal Article
• Authors: Colmenares, Eligio; Neilan, Michael
• Is Part Of: Computers & mathematics with applications. Volume 72:issue 7(2016)
• Page Start: 1828
• Page End: 1850
• Publication Date: 2016-10
• Subjects: Mixed finite element methods -- Boussinesq problem -- Mixed-primal formulation -- Dual-mixed formulation -- A priori estimates; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2016.08.011
• Languages: English
• ISSNs: 0898-1221

Abstract

Abstract: We propose and analyze two mixed approaches for numerically solving the stationary Boussinesq model describing heat driven flows. For the fluid equations, the velocity gradient and a Bernoulli stress tensor are introduced as auxiliary unknowns. For the heat equation, we consider primal and mixed-primal formulations; the latter, incorporating additionally the normal component of the temperature gradient on the Dirichlet boundary. Both dual-mixed formulations exhibit the same classical structure of the Navier–Stokes equations. We derive a priori estimates and the existence of continuous and discrete solutions for the formulations. In addition, we prove the uniqueness of solutions and optimal-order error estimates provided the data is sufficiently small. Numerical experiments are given which back up the theoretical results and illustrate the robustness and accuracy of both methods for a classic benchmark problem.