A posteriori error analysis of the time dependent Navier–Stokes equations with mixed boundary conditions
Tóm tắt
Từ khóa
Tài liệu tham khảo
Abboud, H., El Chami, F., Sayah, T.: A priori and a posteriori estimates for three dimentional Stokes equations with non standard boundary conditions. Numer. Methods Partial Differ. Equ. 28, 1178–1193 (2012)
Amrouche, C., Bernardi, C., Dauge, M., Girault, V.: Vector potentials in three-dimensional nonsmooth domains. Math. Meth. Appl. Sci. 2, 823–864 (1998)
Bänsch, E., Karakatsani, F., Makridakis, Ch.: A posteriori error control for fully discrete Crank–Nicolson schemes. SIAM J. Numer. Anal. 50, 2845–2872 (2012)
Bergam, A., Bernardi, C., Hecht, F., Mghazli, Z.: Error indicators for the mortar finite element discretization of a parabolic problem. Numer. Algorithms 34, 187–201 (2003)
Bernardi, C., Hecht, F., Verfürth, R.: Finite element discretization of the three-dimensional Navier-Stokes equations with mixed boundary conditions. Math. Model. Numer. Anal. 3, 1185–1201 (2009)
Bernardi, C., Maday, Y., Rapetti, F.: Discrétisations variationnelles de problèmes aux limites elliptiques. Collection “Mathématiques et Applications”, vol. 45. Springer, Berlin (2004)
Bernardi, C., Sayah, T.: A posteriori error analysis of the time dependent Stokes equations with mixed boundary conditions. IMA J. Numer. Anal. 35, 179–198 (2015). doi: 10.1093/imanum/drt06
Bernardi, C., Süli, E.: Time and space adaptivity for the second-order wave equation. Math. Models Methods Appl. Sci. 15, 199–225 (2005)
Bernardi, C., Verfürth, R.: A posteriori error analysis of the fully discretized time-dependent Stokes equations. Math. Model. Numer. Anal. 38, 437–455 (2004)
Clément, P.: Approximation by finite element functions using local regularisation. R.A.I.R.O. Anal. Numer. 9, 77–84 (1975)
Costabel, M.: A remark on the regularity of solutions of Maxwell’s equations on Lipschitz domains. Math. Meth. Appl. Sci. 12, 365–368 (1990)
El Chami, F., Sayah, T.: A posteriori error estimators for the fully discrete time dependent Stokes problem with some different boundary conditions. Calcolo 47, 169–192 (2010)
Girault, V., Raviart, P.-A.: Finite Element Approximation of the Navier–Stokes Equations. Lecture Notes in Mathematics, vol. 749. Springer, Berlin (1979)
Girault, V., Raviart, P.-A.: Finite Element Methods for Navier–Stokes Equations. Theory and Algorithms. Springer, Berlin (1986)
Johnson, C., Rannacher, R., Boman, M.: Numerics and hydrodynamic stability: toward error control in computational fluid dynamics. SIAM J. Numer. Anal. 32, 1058–1079 (1995)
Lakkis, O., Makridakis, Ch.: Elliptic reconstruction and a posteriori error estimates for fully discrete linear parabolic problems. Math. Comput. 75, 1627–1658 (2006)
Nochetto, R.H., Savaré, G., Verdi, C.: A posteriori error estimates for variable time-step discretizations of nonlinear evolution equations. Commun. Pure. Math. 53, 525–589 (2000)
Pousin, J., Rappaz, J.: Consistency, stability, a priori and a posteriori errors for Petrov-Galerkin methods applied to nonlinear problems. Numer. Math. 69, 213–231 (1994)
Temam, R.: Navier–Stokes Equations. Theory and Numerical Analysis. Studies in Mathematics and its Applications, vol. 2. North-Holland Publishing Co., Amsterdam (1977)
Verfürth, R.: A Review of A Posteriori Error Estimation and Adaptive Mesh-Refinement Techniques. Wiley, New York (1996)