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arXiv · 2604.06560

Nitsche's method for the stationary Boussinesq system under mixed and nonlinear boundary conditions

Aparna Bansal·Nicolás A. Barnafi·Gianmarco Sperone·Dwijendra N. Pandey
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Abstract

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.

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Aparna Bansal, Nicolás A. Barnafi, Gianmarco Sperone, Dwijendra N. Pandey. 2026-04-08. Nitsche's method for the stationary Boussinesq system under mixed and nonlinear boundary conditions. https://arxiv.org/abs/2604.06560

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