A stabilized finite element methdod for a coupled problem
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In this work, we introduce and analyze a new stabilized finite element scheme for the Stokes–Temperature coupled problem. This new scheme allows equal order of interpolation to approximate the quantities of interest, i.e. velocity, pressure, and temperature. The existence of the discrete solution is proved, decou-pling the proposed stabilized scheme and using the help of continuous dependence results and Brouwer’s theorem under standard assumptions of sufficiently small data. Optimal convergence is proved under classic regularity assumptions of the solution. Finally, we present some numerical examples to show the quality of our scheme, in particular, we compare our results with those coming from a standard reference in geosciences.
