A stabilized finite element method for the Stokes-Temperature coupled problem - Archive ouverte HAL
Pré-Publication, Document De Travail Année : 2022

A stabilized finite element method for the Stokes-Temperature coupled problem

Cristian Cárcamo
  • Fonction : Auteur
  • PersonId : 1176181
Abner Poza
  • Fonction : Auteur
  • PersonId : 986388

Résumé

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, temperature, and stress. We analyze an equivalent variational formulation of the coupled problem inspired by the ideas proposed in [3]. The existence of the discrete solution is proved, decoupling the proposed stabilized scheme and using the help of continuous dependence results and Brouwer's theorem under the standard assumption 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 described in [38].
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Dates et versions

hal-03820068 , version 1 (18-10-2022)

Identifiants

  • HAL Id : hal-03820068 , version 1

Citer

Rodolfo Araya, Cristian Cárcamo, Abner Poza. A stabilized finite element method for the Stokes-Temperature coupled problem. 2022. ⟨hal-03820068⟩

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