Gazca Orozco PA, Süli E, Farrell P (2021)
Publication Language: English
Publication Type: Journal article, Original article
Publication year: 2021
We devise 3-field and 4-field finite element approximations of a system describing the steady state of an incompressible heat-conducting fluid with implicit non-Newtonian rheology. We prove that the sequence of numerical approximations converges to a weak solution of the problem. We develop a block preconditioner based on augmented Lagrangian stabilisation for a discretisation based on the Scott-Vogelius finite element pair for the velocity and pressure. The preconditioner involves a specialised multigrid algorithm that makes use of a space-decomposition that captures the kernel of the divergence and non-standard intergrid transfer operators. The preconditioner exhibits robust convergence behaviour when applied to the Navier-Stokes and power-law systems, including temperature-dependent viscosity, heat conductivity and viscous dissipation.
APA:
Gazca Orozco, P.A., Süli, E., & Farrell, P. (2021). Finite element appoximation and augmented Lagrangian preconditioning for anisothermal implicitly-constituted non-Newtonian flow. Mathematics of Computation.
MLA:
Gazca Orozco, Pablo Alexei, Endre Süli, and Patrick Farrell. "Finite element appoximation and augmented Lagrangian preconditioning for anisothermal implicitly-constituted non-Newtonian flow." Mathematics of Computation (2021).
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