Djoko, J.K. (Jules Kamdem)Konlack, Virginie S.Mbehou, Mohamed2021-02-082021-02-082020-01Djoko JK, Konlack VS, Mbehou M. Stokes equations under nonlinear slip boundary conditions coupled with the heat equation: A priori error analysis. Numerical Methods for Partial Differential Equations 2020;36:86–117. https://doi.org/10.1002/num.22402.0749-159X (print)1098-2426 (online)10.1002/num.22402http://hdl.handle.net/2263/78297In this work, we consider the heat equation coupled with Stokes equations under threshold type boundary condition. The conditions for existence and uniqueness of the weak solution are made clear. Next we formulate the finite element problem, recall the conditions of its solvability, and study its convergence by making use of Babuska–Brezzi's conditions for mixed problems. Third we formulate an Uzawa's type iterative algorithm that separates the fluid from heat conduction, study its feasibility, and convergence. Finally the theoretical findings are validated by numerical simulations.en© 2019 Wiley Periodicals, Inc., A Wiley Company. This is the pre-peer reviewed version of the following article : Stokes equations under nonlinear slip boundary conditions coupled with the heat equation: A priori error analysis. Numerical Methods for Partial Differential Equations 2020;36:86–117. https://doi.org/10.1002/num.22402. The definite version is available at : http://wileyonlinelibrary.com/journal/num.Error estimatesIterative schemeNonlinear slip boundary conditionVariational inequalitiesPostprint Article