Super-convergence of the a posteriori error estimators for finite-element solutions

• Autorzy: C̆iegis R.
• Języki publikacji: EN

Słowa kluczowe

EN

boundary value problem; Galerkin method

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2003
• Tom: Vol. 36, nr 2
• Strony: 495--506
• Opis fizyczny: Bibliogr. 19 poz.

Twórcy

autor

C̆iegis R.

• Institue of Mathematics, Vilnius Gediminas Technical University, Sauletekio Str. 11, LT-2040 Vilnius, Lithuania

Bibliografia

• [1] M. Ainsworth, The influence and selection of subspaces for a posteriori error estimators, Numer. Math., 73 (1996), 399-418.
• [2] M. Ainsworth and J. T. Oden, A posteriori error estimation in finite element analysis, Comput. Methods Appl. Mech. Engrg., 142 (1997), 1-88.
• [3] I. Babuška and W. Rheinboldt, Analysis of optimal finite-element meshes in R¹, Math, of Comp., 33 (1979), 435-463.
• [4] R. E. Bank and A. Weiser, Some a posteriori error estimators for elliptic partial differential equations, Math. Comput., 44 (1985), 283-301.
• [5] R. Becker and R. Rannacher, Weighted a posteriori error control in finite element methods: basic analysis and examples, East-West J. Numer. Math., 4 (1996), 237-264.
• [6] G. F. Carey and J. T. Oden, Finite elements - A second cource. Vol. II., Prentice - Hall, Englewood Cliffs, 1983.
• [7] R. Čiegis, On the accuracy of a posteriori estimates for finite element schemes. In Pitman Research Notes in Mathematics, Series 375, Integral methods in science and engineering, 1997, 74-78.
• [8] K. Eriksson, D. Estep, P. Hansbo and C. Johnson, Introduction to adaptive methods for differential equations. In Acta Numerica 1995, A.Iserles, ed., Cambridge University Press, 1995, 105-158.
• [9] J. Hugger, An asymptotically exact, pointwise, a posteriori error estimator for the finite element method with super convergence properties. In Adaptive methods forPDE, 1993, 277-305.
• [10] K. Eriksson and C. Johnson, Adaptive finite element methods for parabolic problems: I. A linear model problem, SIAM J. Numer. Anal., 28 (1991), 43-77.
• [11] P. Moore and J. Flaherty, A local refinement finite element method for onedimensional parabolic systems, SIAM J. Numer. Anal., 27 (1990), 1422-1444.
• [12] P. Moore, A posteriori error estimation with finite element semi- and fully discrete methods for nonlinear parabolic equations in one space dimension, SIAM J. Numer. Anal., 31 (1994), 149-169.
• [13] C. Johnson, R. Rannacher and M. Boman, Numerics and hydrodynamic stability: towards error control in CFD, SIAM J. Numer. Anal., 32 (1995), 1058-1079.
• [14] A. A. Samarskii, The Theory of Difference Schemes, Nauka, Moscow, 1983 (in Russian).
• [15] V. Thomee, Galerkin Finite Element Methods for Parabolic Problems, Springer-Verlag, Berlin, 1984.
• [16] R. Verfürth, A Review of A Posteriori Error Estimation and Adaptive Mesh-Refinement Techniques, John Wileys/Teubner, New York, Stuttgart, 1996.
• [17] L. B. Wahlbin, Superconvergence in Galerkin Finite Element Methods, Springer, 1991.
• [18] Z. Zhang, Ultraconvergence of the patch recovery technique, Math. Comp., 65 (1996), 1431-1437.
• [19] Z. Zhang, Ultraconvergence of the patch recovery technique II, Math. Comp., 69 (1999), 141-158.