Open Access
Issue |
ESAIM: M2AN
Volume 55, Number 6, November-December 2021
|
|
---|---|---|
Page(s) | 2679 - 2703 | |
DOI | https://doi.org/10.1051/m2an/2021068 | |
Published online | 11 November 2021 |
- M.S. Alnaes, A. Logg, K.B. Ølgaard, M.E. Rognes and G.N. Wells, Unified form language: a domain-specific language for weak formulations of partial differential equations. ACM Trans. Math. Softw. 40 (2014) 1–37. [CrossRef] [Google Scholar]
- P.R. Amestoy, I.S. Duff, J. Koster and J.Y. L’Excellent, A fully asynchronous multifrontal solver using distributed dynamic scheduling. SIAM J. Matrix Anal. Appl. 23 (2001) 15–41. [CrossRef] [MathSciNet] [Google Scholar]
- A. Aposporidis, E. Haber, M.A. Olshanskii and A. Veneziani, A mixed formulation of the Bingham fluid flow problem: analysis and numerical solution. Comput. Methods Appl. Mech. Eng. 200 (2011) 2434–2446. [CrossRef] [Google Scholar]
- N.J. Balmforth, I.A. Frigaard and G. Ovarlez, Yielding to stress: recent developments in viscoplastic fluid mechanics. Ann. Rev. Fluid Mech. 46 (2014) 121–146. [CrossRef] [Google Scholar]
- S. Basu and U.S. Shivhare, Rheological, textural, microstructural, and sensory properties of sorbitol-substituted mango jam. Food Bioprocess. Technol. 6 (2013) 1401–1413. [CrossRef] [Google Scholar]
- M. Bercovier and M. Engelman, A finite-element method for incompressible non-Newtonian flows. J. Comput. Phys. 36 (1980) 313–326. [CrossRef] [MathSciNet] [Google Scholar]
- R.B. Bird, G.C. Dal and B.J. Yarusso, The rheology and flow of viscoplastic materials. Rev. Chem. Eng. 1 (1983) 1–70. [CrossRef] [Google Scholar]
- J. Blechta, J. Málek and K.R. Rajagopal, On the classification of incompressible fluids and a mathematical analysis of the equations that govern their motion. SIAM J. Math. Anal. 52 (2020) 1232–1289. [CrossRef] [MathSciNet] [Google Scholar]
- D. Boffi, F. Brezzi and M. Fortin, Mixed Finite Element Methods and Applications. Springer (2013). [CrossRef] [Google Scholar]
- M. Bulíček, P. Gwiazda, J. Málek and A. Świerczewska-Gwiazda, On steady flows of incompressible fluids with implicit power-law-like rheology. Adv. Calc. Var. 2 (2009) 109–136. [MathSciNet] [Google Scholar]
- M. Bulíček, P. Gwiazda, J. Málek and A. Świerczewska-Gwiazda, On unsteady flows of implicitly constituted incompressible fluids. SIAM J. Math. Anal. 44 (2012) 2756–2801. [CrossRef] [MathSciNet] [Google Scholar]
- M. Bulíček, J. Burczak and S. Schwarzacher, A unified theory for some non-Newtonian fluids under singular focing. SIAM J. Math. Anal. 48 (2016) 4241–4267. [CrossRef] [MathSciNet] [Google Scholar]
- M. Bulíček, J. Málek and E. Maringová, On nonlinear problems of parabolic type with implicit constitutive equations involving flux. Math. Models Methods Appl. Sci. (2021) 1–52. DOI: 10.1142/S0218202521500457. [Google Scholar]
- X. Chen, Z. Nashed and L. Qi, Smoothing methods and semismooth methods for non-differentiable operator equations. SIAM J. Numer. Anal. 38 (2000) 1200–1216. [CrossRef] [MathSciNet] [Google Scholar]
- F.H. Clarke, Optimization and Nonsmooth Analysis. Wiley, New York (1983). [Google Scholar]
- J.C. De lo Reyes and S.G. Andrade, Numerical simulation of two-dimensional Bingham fluid flow by semismooth Newton methods. J. Comput. Appl. Math. 235 (2010) 11–32. [CrossRef] [MathSciNet] [Google Scholar]
- J.C. De los Reyes and M. Hintermüller, A duality based semismooth Newton framework for solving variational inequalities of the second kind. Interfaces Free Boundaries 13 (2011) 437–462. [CrossRef] [MathSciNet] [Google Scholar]
- L. Diening, C. Kreuzer and E. Süli, Finite element approximation of steady flows of incompressible fluids with implicit power-law-like rheology. SIAM J. Numer. Anal. 51 (2013) 984–1015. [Google Scholar]
- Y. Dimakopoulos, G. Makrigiorgos, G.C. Georgiou and J. Tsamopoulos, The PAL (Penalized Augmented Lagrangian) method for computing viscoplastic flows: a new fast converging scheme. J. Non-Newt. Fluid Mech. 256 (2018) 23–41. [CrossRef] [Google Scholar]
- P.E. Farrell and P.A. Gazca-Orozco, Augmented Lagrangian preconditioner for implicitly-constituted non-Newtonian incompressible flow. SIAM J. Sci. Comput. 42 (2020) B1329–B1349. [CrossRef] [Google Scholar]
- P.E. Farrell, P.A. Gazca-Orozco and E. Süli, Numerical analysis of unsteady implicitly constituted incompressible fluids: 3-field formulation. SIAM J. Numer. Anal. 58 (2020) 757–787. [CrossRef] [MathSciNet] [Google Scholar]
- I.A. Frigaard and C. Nouar, On the usage of viscosity regularisation methods for viscoplastic fluid flow computation. J. Non-Newt. Fluid Mech. 127 (2005) 1–26. [CrossRef] [Google Scholar]
- M. Fuchs and G. Seregin, Variational methods for fluids of Prandtl-Eyring type and plastic materials with logarithmic hardening. Math. Methods Appl. Sci. 22 (1999) 317–351. [CrossRef] [MathSciNet] [Google Scholar]
- M. Fuchs and G. Seregin, Variational Methods for Problems from Plasticity Theory and for Generalized Newtonian Fluids. Lecture Notes in Math. 1749. Springer Verlag (2000). [CrossRef] [Google Scholar]
- V. Girault and P.A. Raviart, Finite Element Methods for Navier-Stokes Equations: Theory and Algorithms. Springer Verlag (1986). [CrossRef] [Google Scholar]
- R. Glowinski and A. Wachs, On the numerical simulation of viscoplastic fluid flow. In: Vol. XVI of Handbook of Numerical Analysis. Numerical Methods for Non-Newtonian Fluids. North Holland (2010) 483–718. [Google Scholar]
- H. Goldberg, W. Kampowsky and F. Tröltzsch, On Nemytskij operators in Lp-spaces of abstract functions. Math. Nachr. 155 (1992) 127–140. [CrossRef] [MathSciNet] [Google Scholar]
- P.P. Grinevich and M.A. Olshanskii, An iterative method for the Stokes-type problem with variable viscosity. SIAM J. Sci. Comput. 31 (2009) 3959–3978. [CrossRef] [MathSciNet] [Google Scholar]
- L.H. Luu and Y. Forterre, Drop impact of yield-stress fluids. J. Fluid Mech. 632 (2009) 301–327. [CrossRef] [Google Scholar]
- E. Maringová and J. Žabenský, On a Navier–Stokes–Fourier-like system capturing transitions between viscous and inviscid fluid regimes and between no-slip and perfect-slip boundary conditions. Nonlinear Anal. Real World Appl. 41 (2018) 152–178. [CrossRef] [MathSciNet] [Google Scholar]
- A. Marly and P. Vigneaux, Augmented Lagrangian simulations study of yield-stress fluid flows in expansion-contraction and comparisons with physical experiments. J. Non-Newtonian Fluid Mech. 239 (2017) 35–52. [CrossRef] [MathSciNet] [Google Scholar]
- R. Mifflin, Semismooth and semiconvex functions in constrained optimization. SIAM J. Control Optim. 15 (1977) 959–972. [CrossRef] [MathSciNet] [Google Scholar]
- A. Putz, I.A. Frigaard and D.M. Martínez, On the lubrication paradox and the use of regularisation methods for lubrication flows. J. Non-Newt. Fluid Mech. 163 (2009) 62–77. [CrossRef] [Google Scholar]
- L.Q. Qi, Convergence analysis of some algorithms for solving nonsmooth equations. Math. Oper. Res. 18 (1993) 227–244. [CrossRef] [MathSciNet] [Google Scholar]
- L.Q. Qi and J. Sun, A nonsmooth version of Newton’s method. Math. Program. 58 (1993) 353–367. [CrossRef] [Google Scholar]
- J. Qin, On the convergence of some low order mixed finite elements for incompressible fluids. Ph.D. thesis, Pennsylvania State University (1994). [Google Scholar]
- K.R. Rajagopal, On implicit constitutive theories. Appl. Math. 48 (2003) 279–319. [CrossRef] [MathSciNet] [Google Scholar]
- K.R. Rajagopal, On implicit constitutive theories for fluids. J. Fluid Mech. 550 (2006) 243–249. [CrossRef] [MathSciNet] [Google Scholar]
- K.R. Rajagopal and A.R. Srinivasa, On the thermodynamics of fluids defined by implicit constitutive relations. Z. Angew. Math. Phys. 59 (2008) 715–729. [CrossRef] [MathSciNet] [Google Scholar]
- F. Rathgeber, D.A. Ham, L. Mitchell, M. Lange, F. Luporini, A.T.T. Mcrae, G.-T. Bercea, G.R. Markall and P.H.J. Kelly, Firedrake: automating the finite element method by composing abstractions. ACM Trans. Math. Softw. 43 (2016) 1–27. [Google Scholar]
- P. Saramito, A damped Newton algorithm for computing viscoplastic fluid flows. J. Non-Newt. Fluid Mech. 238 (2016) 6–15. [CrossRef] [Google Scholar]
- P. Saramito and A. Wachs, Progress in numerical simulation of yield stress fluid flows. Rheol. Acta 56 (2017) 211–230. [CrossRef] [Google Scholar]
- A. Schiela, A simplified approach to semismooth Newton methods in function space. SIAM J. Optim. 19 (2008) 1417–1432. [CrossRef] [MathSciNet] [Google Scholar]
- E. Süli and T. Tscherpel, Fully discrete finite element approximation of unsteady flows of implicitly constituted incompressible fluids. IMA J. Numer. Anal. 40 (2021) 801–849. [Google Scholar]
- A. Syrakos, G.C. Georgiou and A.N. Alexandrou, Solution of the square lid-driven cavity flow of a Bingham plastic using the finite volume method. J. Non-Newtonian Fluid Mech. 195 (2013) 19–31. [CrossRef] [Google Scholar]
- T. Treskatis, A. Roustaei, I. Frigaard and A. Wachs, Practical guidelines for fast, efficient and robust simulations of yield-stress flows without regularisation: a study of accelerated proximal gradient and augmented Lagrangian methods. J. Non-Newtonian Fluid Mech. 262 (2018) 149–164. [CrossRef] [MathSciNet] [Google Scholar]
- F. Tröltzsch, Optimal Control of Partial Differential Equations: Theory, Methods, and Applications, American Mathematical Soc. Vol. 112 (2010). [Google Scholar]
- T. Tscherpel, FEM for the unsteady flow of implicitly constituted incompressible fluids. Ph.D. thesis. University of Oxford (2018). [Google Scholar]
- M. Ulbrich, Semismooth Newton methods for operator equations in function spaces. SIAM J. Optim. 13 (2003) 805–841. [Google Scholar]
- M. Ulbrich, Semismooth Newton Methods for Variational Inequalities and Constrained Optimization Problems in Function Spaces. MOS-SIAM Series on Optimization. SIAM (2011). [Google Scholar]
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.