Analysis of a semi-augmented mixed finite element method for double-diffusive natural convection in porous media

06/05/2021
by   Mario Álvarez, et al.
0

In this paper we study a stationary double-diffusive natural convection problem in porous media given by a Navier-Stokes/Darcy type system, for describing the velocity and the pressure, coupled to a vector advection-diffusion equation describing the heat and substance concentration, of a viscous fluid in a porous media with physical boundary conditions. The model problem is rewritten in terms of a first-order system, without the pressure, based on the introduction of the strain tensor and a nonlinear pseudo-stress tensor in the fluid equations. After a variational approach, the resulting weak model is then augmented using appropriate redundant penalization terms for the fluid equations along with a standard primal formulation for the heat and substance concentration. Then, it is rewritten as an equivalent fixed-point problem. Well-posedness and uniqueness results for both the continuous and the discrete schemes are stated, as well as the respective convergence result under certain regularity assumptions combined with the Lax-Milgram theorem, and the Banach and Brouwer fixed-point theorems. In particular, Raviart-Thomas elements of order k are used for approximating the pseudo-stress tensor, piecewise polynomials of degree ≤ k and ≤ k+1 are utilized for approximating the strain tensor and the velocity, respectively, and the heat and substance concentration are approximated by means of Lagrange finite elements of order ≤ k+1. Optimal a priori error estimates are derived and confirmed through some numerical examples that illustrate the performance of the proposed semi-augmented mixed-primal scheme.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 27

page 28

11/28/2021

Augmented finite element formulation for the Navier–Stokes equations with vorticity and variable viscosity

We propose and analyse an augmented mixed finite element method for the ...
03/01/2022

Error estimates for a vorticity-based velocity-stress formulation of the Stokes eigenvalue problem

The aim of this paper is to analyze a mixed formulation for the two dime...
08/26/2019

Advection-diffusion-reaction in poroelastic media. Part I: Well-posedness and discrete analysis

We analyse a PDE system modelling poromechanical processes (formulated i...
08/26/2019

Well-posedness and discrete analysis for advection-diffusion-reaction in poroelastic media

We analyse a PDE system modelling poromechanical processes (formulated i...
09/30/2021

Twofold saddle-point formulation of Biot poroelasticity with stress-dependent diffusion

We introduce a stress/total-pressure formulation for poroelasticity that...
01/19/2021

Combined Newton-Raphson and Streamlines-Upwind Petrov-Galerkin iterations for nano-particles transport in buoyancy driven flow

The present study deals with the finite element discretization of nanofl...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.