FINITE ELEMENT APPROXIMATION AND PRECONDITIONING FOR ANISOTHERMAL FLOW OF IMPLICITLY-CONSTITUTED NON-NEWTONIAN FLUIDS
Farrell P, Orozco PAG, Suli E (2022)
Publication Type: Journal article
Publication year: 2022
Journal
Book Volume: 91
Pages Range: 659-697
Journal Issue: 334
DOI: 10.1090/mcom/3703
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.
Involved external institutions
United Kingdom (GB)How to cite
APA:
Farrell, P., Orozco, P.A.G., & Suli, E. (2022). FINITE ELEMENT APPROXIMATION AND PRECONDITIONING FOR ANISOTHERMAL FLOW OF IMPLICITLY-CONSTITUTED NON-NEWTONIAN FLUIDS. Mathematics of Computation, 91(334), 659-697. https://dx.doi.org/10.1090/mcom/3703
MLA:
Farrell, Patrick, Pablo Alexei Gazca Orozco, and Endre Suli. "FINITE ELEMENT APPROXIMATION AND PRECONDITIONING FOR ANISOTHERMAL FLOW OF IMPLICITLY-CONSTITUTED NON-NEWTONIAN FLUIDS." Mathematics of Computation 91.334 (2022): 659-697.
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