An adaptive stabilized finite element method for the Darcy’s equations with pressure dependent viscosities

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

“…Again, based on the assumption of small data, the existence of the discrete solution can be stated using Brouwer's fixed point theorem. Optimal convergence of the proposed scheme is proved using standard nonlinear finite element results (for a similar result of a stabilized scheme applied to a nonlinear Darcy equation, see [5]).…”

“…−y 2 , z 2 , x 2 ), p(x, y, z) = −0.125 + xyz, and ϕ(x, y, z) = 0.1 − 0.3e −xyz , where the velocity as well the pressure have been taken from[5]. The viscosity is given by µ(r) = 0.5e 0.1/r and the thermal conductivity used is k = 1.…”