Free Access
Issue
ESAIM: M2AN
Volume 55, Number 2, March-April 2021
Page(s) 659 - 687
DOI https://doi.org/10.1051/m2an/2021005
Published online 31 March 2021
  1. S. Agmon, Lectures on Elliptic Boundary Value Problems. Van Nostrand, Princeton, NJ (1965). [Google Scholar]
  2. A. Allendes, E. Otárola and A. Salgado, A posteriori error estimates for the stationary Navier-Stokes equations with Dirac measures. SIAM J. Sci. Comput. 42 (2020) A1860–A1884. [Google Scholar]
  3. M. Alvarez, G.N. Gatica and R. Ruiz-Baier, A posteriori error analysis for a viscous flow-transport problem. ESAIM: M2AN 50 (2016) 1789–1816. [EDP Sciences] [Google Scholar]
  4. I. Babuška and G.N. Gatica, A residual-based a posteriori error estimator for the Stokes-Darcy coupled problem. SIAM J. Numer. Anal. 48 (2010) 498–523. [Google Scholar]
  5. F. Brezzi and M. Fortin, Mixed and Hybrid Finite Element Methods. In: Vol. 15 of Springer Series in Computational Mathematics. Springer-Verlag, New York (1991). [Google Scholar]
  6. J. Camaño, C. García and R. Oyarzúa, Analysis of a momentum conservative mixed-FEM for the stationary Navier-Stokes problem. To appear in: Numer. Meth. Partial Differ. Equ. (2021). [Google Scholar]
  7. C. Carstensen, A posteriori error estimate for the mixed finite element method. Math. Comp. 66 (1997) 465–476. [Google Scholar]
  8. S. Caucao, D. Mora and R. Oyarzúa, A priori and a posteriori error analysis of a pseudostress-based mixed formulation of the Stokes problem with varying density. IMA J. Numer. Anal. 36 (2016) 947–983. [Google Scholar]
  9. S. Caucao, G.N. Gatica and R. Oyarzúa, A posteriori error analysis of a fully-mixed formulation for the Navier–Stokes/Darcy coupled problem with nonlinear viscosity. Comput. Methods Appl. Mech. Eng. 315 (2017) 943–971. [Google Scholar]
  10. S. Caucao, G.N. Gatica, R. Oyarzúa and F. Sandoval, Residual-based A Posteriori Error Analysis for the Coupling of the Navier–Stokes and Darcy–Forchheimer Equations. Centro de Investigación en Ingeniería Matemática (CI2MA), Universidad de Concepción, Chile. Preprint 2019-33 (2019). [Google Scholar]
  11. S. Caucao, M. Discacciati, G.N. Gatica and R. Oyarzúa, A conforming mixed finite element method for the Navier–Stokes/Darcy–Forchheimer coupled problem. ESAIM: M2AN 54 (2020) 1689–1723. [EDP Sciences] [Google Scholar]
  12. P. Clément, Approximation by finite element functions using local regularisation. RAIRO Modél. Math. Anal. Numér. 9 (1975) 77–84. [Google Scholar]
  13. E. Creuse, M. Farhloul and L. Paquet, A posteriori error estimation for the dual mixed finite element method for the p-Laplacian in a polygonal domain. Comput. Methods Appl. Mech. Eng. 196 (2007) 2570–2582. [Google Scholar]
  14. C. Domínguez, G.N. Gatica and S. Meddahi, A posteriori error analysis of a fully-mixed finite element method for a two-dimensional fluid-solid interaction problem. J. Comput. Math. 33 (2015) 606–641. [Google Scholar]
  15. F. Durango and J. Novo, A posteriori error estimations for mixed finite element approximations to the Navier–Stokes equations based on Newton-type linearization. J. Comput. Appl. Math. 367 (2020). [Google Scholar]
  16. A. Ern and J.-L. Guermond, Theory and Practice of Finite Elements. In: Vol. 159 of Applied Mathematical Sciences. Springer-Verlag, New York (2004). [Google Scholar]
  17. V.J. Ervin and T.N. Phillips, Residual a posteriori error estimator for a three-field model of a non-linear generalized Stokes problem. Comput. Methods Appl. Mech. Engrg. 195 (2006) 2599–2610. [Google Scholar]
  18. M. Farhloul and A.M. Zine, A posteriori error estimation for a dual mixed finite element approximation of non-Newtonian fluid flow problems. Int. J. Numer. Anal. Model. 5 (2008) 320–330. [Google Scholar]
  19. M. Farhloul, S. Nicaise and L. Paquet, A priori and a posteriori error estimations for the dual mixed finite element method of the Navier-Stokes problem. Numer. Methods Part. Differ. Equ. 25 (2009) 843–869. [Google Scholar]
  20. G.N. Gatica, A Simple Introduction to the Mixed Finite Element Method. Theory and Applications. Springer Briefs in Mathematics. Springer, Cham (2014). [Google Scholar]
  21. G.N. Gatica, G.C. Hsiao and S. Meddahi, A residual-based a posteriori error estimator for a two-dimensional fluid-solid interaction problem. Numer. Math. 114 (2009) 63–106. [Google Scholar]
  22. G.N. Gatica, R. Ruiz-Baier and G. Tierra, A posteriori error analysis of an augmented mixed method for the Navier-Stokes equations with nonlinear viscosity. Comput. Math. Appl. 72 (2016) 2289–2310. [Google Scholar]
  23. L.F. Gatica, R. Oyarzúa and N. Sánchez, A priori and a posteriori error analysis of an augmented mixed-FEM for the Navier–Stokes–Brinkman problem. Comput. Math. Appl. 75 (2018) 2420–2444. [Google Scholar]
  24. V. Girault and P.A. Raviart, Finite Element Methods for Navier–Stokes Equations. Theory and Algorithms. In: Vol. 5 of Springer Series in Computational Mathematics. Springer-Verlag, Berlin (1986). [Google Scholar]
  25. P. Grisvard, Elliptic Problems in Nonsmooth Domains. In: Vol. 24 of Monographs and Studies in Mathematics. Pitman (Advanced Publishing Program), Boston, MA (1985). [Google Scholar]
  26. F. Hecht, New development in freefem++. J. Numer. Math. 20 (2012) 251–265. [Google Scholar]
  27. F. Hecht, Freefem++, 3rd edition, Version 3.58-1. Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, Paris (2018). [available in http://www.freefem.org/ff++]. [Google Scholar]
  28. G. Kanschat and D. Schötzau, Energy norm a posteriori error estimation for divergence-free discontinuous Galerkin approximations of the Navier-Stokes equations. Inter. J. Numer. Methods Fluids 57 (2008) 1093–1113. [Google Scholar]
  29. J.T. Oden, W. Wu and M. Ainsworth, An a posteriori error estimate for finite element approximations of the Navier-Stokes equations. Comput. Methods Appl. Mech. Engrg. 111 (1994) 185–202. [Google Scholar]
  30. R. Verfürth, A Review of A-Posteriori Error Estimation and Adaptive Mesh-Refinement Techniques. Wiley Teubner, Chichester (1996). [Google Scholar]
  31. R. Verfürth, A Posteriori Error Estimation Techniques for Finite Element Methods. Numerical Mathematics and Scientific Computation. Oxford University Press, Oxford (2013). [Google Scholar]

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