Open Access
Volume 58, Number 2, March-April 2024
Page(s) 457 - 488
Published online 09 April 2024
  1. R. Adams and J. Fournier, Cone conditions and properties of Sobolev spaces. J. Math. Anal. App. 61 (1977) 713–734. [Google Scholar]
  2. N. Ahmed and G. Matthies, Higher-order discontinuous Galerkin time discretizations for the evolutionary Navier–Stokes equations. IMA J. Numer. Anal. 41 (2021) 3113–3144. [Google Scholar]
  3. H. Amann, Linear parabolic problems involving measures. Real Academia de Ciencias Exactas, Fisicas y Naturales. Revista. Serie A, Matematicas 95 (2001) 85–119. [Google Scholar]
  4. D. Arndt, H. Dallmann and G. Lube, Local projection FEM stabilization for the time-dependent incompressible Navier–Stokes problem. Numer. Methods Part. Differ. Equ. 31 (2015) 1224–1250. [Google Scholar]
  5. D. Arndt, H. Dallmann and G. Lube, Quasi-optimal error estimates for the incompressible Navier–Stokes problem discretized by finite element methods and pressure-correction projection with velocity stabilization. Preprint arXiv:1609.00807 (2016). [Google Scholar]
  6. A. Ashyralyev and P.E. Sobolevskii, Well-Posedness of Parabolic Difference Equations. Birkh¨auser Basel (1994). [Google Scholar]
  7. N. Behringer, B. Vexler and D. Leykekhman, Fully discrete best-approximation-type estimates in L(I; L2(Ω)d) for finite element discretizations of the transient Stokes equations. IMA J. Numer. Anal. 43 (2022) 852–880. [Google Scholar]
  8. J. Bergh and J. Löfström, Interpolation Spaces: An Introduction. Vol. 223 of Grundlehren der mathematischen Wissenschaften. Springer Berlin Heidelberg (1976). [Google Scholar]
  9. C. Bernardi and G. Raugel, A conforming finite element method for the time-dependent Navier–Stokes equations. SIAM J. Numer. Anal. 22 (1985) 455–473. [Google Scholar]
  10. I. Bihari, A generalization of a lemma of Bellman and its application to uniqueness problems of differential equations. Acta Math. Acad. Sci. Hung. 7 (1956) 81–94. [Google Scholar]
  11. H. Brezis and P. Mironescu, Gagliardo–Nirenberg inequalities and non-inequalities: the full story. Annales de l’Institut Henri Poincaré C, Analyse non linéaire 35 (2018) 1355–1376. [Google Scholar]
  12. M. Brokate and G. Kersting, Measure and Integral. Springer International Publishing (2015). [Google Scholar]
  13. E. Casas and K. Chrysafinos, A discontinuous Galerkin time-stepping scheme for the velocity tracking problem. SIAM J. Numer. Anal. 50 (2012) 2281–2306. [Google Scholar]
  14. E. Casas and K. Chrysafinos, Analysis of the velocity tracking control problem for the 3D evolutionary Navier–Stokes equations. SIAM J. Control Optim. 54 (2016) 99–128. [Google Scholar]
  15. E. Casas and K. Kunisch, Well-posedness of evolutionary Navier–Stokes equations with forces of low regularity on two-dimensional domains. ESAIM: Control Optim. Calculus Variations 27 (2021). [Google Scholar]
  16. K. Chrysafinos and N. Walkington, Discontinuous Galerkin approximations of the Stokes and Navier–Stokes equations. Math. Comput. 79 (2010) 2135–2167. [Google Scholar]
  17. M. Dauge, Stationary Stokes and Navier–Stokes systems on two- or three-dimensional domains with corners. Part I. Linearized equations. SIAM J. Math. Anal. 20 (1989) 74–97. [Google Scholar]
  18. J. De Frutos, B. García-Archilla, V. John and J. Novo, Error analysis of non inf-sup stable discretizations of the time-dependent Navier–Stokes equations with local projection stabilization. IMA J. Numer. Anal. 39 (2019) 1747–1786. [Google Scholar]
  19. L. de Simon, Un’applicazione della teoria degli integrali singolari allo studio delle equazioni differenziali lineari astratte del primo ordine. Rendiconti del Seminario Matematico della Università di Padova 34 (1964) 205–223. [Google Scholar]
  20. K. Deckelnick and M. Hinze, Semidiscretization and error estimates for distributed control of the instationary Navier–Stokes equations. Numer. Math. 97 (2004) 297–320. [Google Scholar]
  21. F. Demengel and G. Demengel, Functional Spaces for the Theory of Elliptic Partial Differential Equations. Universitext, Springer London, (2012). [Google Scholar]
  22. K. Disser, A. ter Elst and J. Rehberg, Hölder estimates for parabolic operators on domains with rough boundary. Annali Scuola Normale Superiore di Pisa, Classe di Scienze XVII (2017) 65–79. [Google Scholar]
  23. E. Emmrich, Error of the two-step BDF for the incompressible Navier–Stokes problem. ESAIM: Math. Modell. Numer. Anal. 38 (2004) 757–764. [Google Scholar]
  24. K. Eriksson, C. Johnson and V. Thomée, Time discretization of parabolic problems by the discontinuous Galerkin method. ESAIM: Math. Modell. Numer. Anal. 19 (1985) 611–643. [Google Scholar]
  25. F. Gabel and P. Tolksdorf, The Stokes operator in two-dimensional bounded Lipschitz domains. J. Differ. Equ. 340 (2022) 227–272. [Google Scholar]
  26. G. Galdi, An Introduction to the Mathematical Theory of the Navier–Stokes Equations. Springer Monographs in Mathematics. Springer New York (2011). [Google Scholar]
  27. V. Girault and P.-A. Raviart, Finite Element Methods for Navier-Stokes Equations. Vol. 5 of Springer Series in Computational Mathematics. Springer Berlin Heidelberg (1986). [Google Scholar]
  28. J.-L. Guermond and J.E. Pasciak, Stability of discrete Stokes operators in fractional Sobolev spaces. J. Math. Fluid Mech. 10 (2008) 588–610. [Google Scholar]
  29. A. Hansbo, Strong stability and non-smooth data error estimates for discretizations of linear parabolic problems. BIT Numer. Math. 42 (2002) 351–379. [Google Scholar]
  30. J.G. Heywood and R. Rannacher, Finite element approximation of the nonstationary Navier–Stokes problem. I. Regularity of solutions and second-order error estimates for spatial discretization. SIAM J. Numer. Anal. 19 (1982) 275–311. [Google Scholar]
  31. J.G. Heywood and R. Rannacher, Finite element approximation of the nonstationary Navier–Stokes problem, part II: stability of solutions and error estimates uniform in time. SIAM J. Numer. Anal. 23 (1986) 750–777. [Google Scholar]
  32. J.G. Heywood and R. Rannacher, Finite-element approximation of the nonstationary Navier–Stokes problem part IV: error analysis for second order time discretization. SIAM J. Numer. Anal. 27 (1990) 353–384. [Google Scholar]
  33. R. Kellogg and J. Osborn, A regularity result for the Stokes problem in a convex polygon. J. Funct. Anal. 21 (1976) 397–431. [Google Scholar]
  34. K. Kirk, T. Horváth and S. Rhebergen, Analysis of an exactly mass conserving space-time hybridized discontinuous Galerkin method for the time-dependent Navier–Stokes equations. Math. Comput. 92 (2022) 525–556. [Google Scholar]
  35. D. Leykekhman and B. Vexler, Discrete maximal parabolic regularity for Galerkin finite element methods. Numer. Math. 135 (2017) 923–952. [Google Scholar]
  36. D. Leykekhman and B. Vexler, L2(I; H1(Ω)) and L2(I; L2(Ω)) best approximation type error estimates for Galerkin solutions of transient Stokes problems. Calcolo 61 (2024) 7. [Google Scholar]
  37. D. Leykekhman, B. Vexler and D. Walter, Numerical analysis of sparse initial data identification for parabolic problems. ESAIM: Math. Modell. Numer. Anal. 54 (2020) 1139–1180. [Google Scholar]
  38. Z. Li, Some generalized Gronwall–Bellman type difference inequalities and applications. J. Math. Inequalities 15 (2021) 173–200. [Google Scholar]
  39. O. Lipovan, A retarded Gronwall-like inequality and its applications. J. Math. Anal. App. 252 (2000) 389–401. [Google Scholar]
  40. A. Lunardi, Analytic Semigroups and Optimal Regularity in Parabolic Problems. Modern Birkh¨auser classics. Birkh¨auser (2012). [Google Scholar]
  41. E. Magenes, Interpolational spaces and partial differential equations. Uspekhi Mat. Nauk 21 (1966) 169–218. [Google Scholar]
  42. D. Meidner, R. Rannacher and B. Vexler, A priori error estimates for finite element discretizations of parabolic optimization problems with pointwise state constraints in time. SIAM J. Control Optim. 49 (2011) 1961–1997. [Google Scholar]
  43. B. Pachpatte, Integral and Finite Difference Inequalities and Applications. Vol. 205 of North-Holland Mathematics Studies. Elsevier (2006). [Google Scholar]
  44. A.H. Schatz and L.B. Wahlbin, Interior maximum-norm estimates for finite element methods, part II. Math. Comput. 64 (1995) 907. [Google Scholar]
  45. F. Schieweck and L. Tobiska, An optimal order error estimate for an upwind discretization of the Navier–Stokes equations. Numer. Methods Part. Differ. Equ. 12 (1996) 407–421. [Google Scholar]
  46. J. Shen, On error estimates of projection methods for Navier–Stokes equations: first-order schemes. SIAM J. Numer. Anal. 29 (1992) 57–77. [Google Scholar]
  47. H. Sohr, The Navier–Stokes Equations. Springer Basel (2001). [Google Scholar]
  48. R. Temam, Navier–Stokes Equations: Theory and Numerical Analysis. North-Holland Publ. Co., Amsterdam (1977). [Google Scholar]
  49. V. Thomée, Galerkin Finite Element Methods for Parabolic Problems. Vol. 25 of Springer Series in Computational Mathematics, 2nd edition. Springer (2006). [Google Scholar]
  50. H. Triebel, Theory of Function Spaces II. Springer Basel (1992). [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.

Recommended for you