Finite element appoximation and augmented Lagrangian preconditioning for anisothermal implicitly-constituted non-Newtonian flow
Gazca Orozco PA, Süli E, Farrell P (2024)
Publication Language: English
Publication Status: Accepted
Publication Type: Unpublished / Preprint
Future Publication Type: Journal article
Publication year: 2024
Publisher: Mathematics of Computation
Open Access Link: https://arxiv.org/abs/2011.03024
Abstract
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.
Authors with CRIS profile
Pablo Alexei Gazca Orozco
Lehrstuhl für Dynamics, Control, Machine Learning and Numerics (Alexander von Humboldt-Professur)
Involved external institutions
United Kingdom (GB)How to cite
APA:
Gazca Orozco, P.A., Süli, E., & Farrell, P. (2024). Finite element appoximation and augmented Lagrangian preconditioning for anisothermal implicitly-constituted non-Newtonian flow. (Unpublished, Accepted).
MLA:
Gazca Orozco, Pablo Alexei, Endre Süli, and Patrick Farrell. Finite element appoximation and augmented Lagrangian preconditioning for anisothermal implicitly-constituted non-Newtonian flow. Unpublished, Accepted. 2024.
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