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Comp."],"abstract":"<p>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\u2013Vogelius 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\u2013Stokes and power-law systems, including temperature-dependent viscosity, heat conductivity and viscous dissipation.<\/p>","DOI":"10.1090\/mcom\/3703","type":"journal-article","created":{"date-parts":[[2021,9,29]],"date-time":"2021-09-29T13:16:07Z","timestamp":1632921367000},"page":"659-697","source":"Crossref","is-referenced-by-count":8,"title":["Finite element approximation and preconditioning for anisothermal flow of implicitly-constituted non-Newtonian fluids"],"prefix":"10.1090","volume":"91","author":[{"given":"Patrick","family":"Farrell","sequence":"first","affiliation":[]},{"given":"Pablo Alexei","family":"Gazca Orozco","sequence":"additional","affiliation":[]},{"given":"Endre","family":"S\u00fcli","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2021,11,23]]},"reference":[{"issue":"1","key":"1","doi-asserted-by":"publisher","first-page":"15","DOI":"10.1137\/S0895479899358194","article-title":"A fully asynchronous multifrontal solver using distributed dynamic scheduling","volume":"23","author":"Amestoy, Patrick R.","year":"2001","journal-title":"SIAM J. 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