Nitsche's method for the stationary Boussinesq system under mixed and nonlinear boundary conditions
This work addresses a domain-specific problem in computational fluid dynamics, providing incremental improvements for simulations in complex geometries.
The paper tackles the stationary Boussinesq system with mixed and nonlinear boundary conditions by analyzing Nitsche's method, establishing well-posedness, optimal convergence rates, and efficient error estimators, validated through numerical tests.
In this paper we analyze Nitsche's method for the stationary Boussinesq system with Navier's slip and a nonlinear boundary condition. Our analysis of the formulation establishes the robustness of a finite elements scheme in arbitrarily complex boundaries. The well-posedness of the discrete problem is established using fixed-point theorems under a standard smallness assumption on the data. We also provide optimal convergence rates for the approximation error. Furthermore, the efficiency and reliability of residual-based a posteriori error estimators are established. We validate our theory through several numerical tests.