The h-p version of the finite element method with quasiuniform meshes
Babuška, I. ; Suri, Manil
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 21 (1987), p. 199-238 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU) 
@article{M2AN_1987__21_2_199_0,
     author = {Babu\v ska, I. and Suri, Manil},
     title = {The $h-p$ version of the finite element method with quasiuniform meshes},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     volume = {21},
     year = {1987},
     pages = {199-238},
     mrnumber = {896241},
     zbl = {0623.65113},
     language = {en},
     url = {http://dml.mathdoc.fr/item/M2AN_1987__21_2_199_0}
}

Babuška, I.; Suri, Manil. The $h-p$ version of the finite element method with quasiuniform meshes. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 21 (1987) pp. 199-238. http://gdmltest.u-ga.fr/item/M2AN_1987__21_2_199_0/

[1] I. Babuska and A. K. Aziz, Survey Lectures on the Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations (A. K. Aziz, ed.), 3-359, Academic Press, New York, 1972. | MR 421106 | Zbl 0268.65052

[2] I. Babuska, M. R. Dorr, Error estimates for the combined h and p versions of finite element method. Numer. Math. 37 (1981), 252-277. | MR 623044 | Zbl 0487.65058

[3] I. Babuska, W. Gui, B. Guo, B. A. Szabo, Theory and performance of the h-p version of the finite element method. To appear.

[4] I. Babuska, R. B. Kellogg, J. Pitkäranta, Direct and inverse error estimates for finite element method. . SIAM J. Numer. Anal. 18 (1981), 515-545. | Zbl 0487.65059

[5] I. Babuska, M. Suri, The optimal convergence rate of the p-version of the finite element method. Tech. Note BN-1045, Institute for Physical Science and Technology, University of Maryland, Oct. 1985. | Zbl 0637.65103

[6] I. Babuska, B. A. Szabo and I. N. Katz, The p-version of the finite element method. SIAM J. Numer. Anal. 18 (1981), 515-545. | MR 615529 | Zbl 0487.65059

[7] I. Babuska and B. A. Szabo, On the rate of convergence of finite element method. Internat. J. Numer. Math. Engrg. 18 (1982), 323-341. | MR 648550 | Zbl 0498.65050

[8] I. Bergh and J. Lofstrom, Interpolation Spaces. Springer, Berlin, Heidelberg, New York, 1976. | Zbl 0344.46071

[9] P. G. Ciarlet, The Finite Element Method for Elliptic Problems. North-Holland, 1978. | MR 520174 | Zbl 0383.65058

[10] M. R. Dorr, The approximation theory for the p-version of the finite element method. SIAM J. Numer. Anal. 21 (1984), 1180-1207. | MR 765514 | Zbl 0572.65074

[11] M. R. Dorr, The Approximation of the Solutions of Elliptic Boundary-Value Problems via the p-Version of the Finite Element Method. SIAM J. Numer. Anal. 23 (1986), 58-77. | MR 821906 | Zbl 0617.65109

[12] P. Grisvard, Elliptic problems in nonsmooth domains. Pitman, Boston, 1985. | MR 775683 | Zbl 0695.35060

[13] W. Gui and I. Babuska, The h, p and h-p versions of the finite element method for one dimensional problem : Part 1 : The error analysis of the p-version. Tech. Note BN-1036 ; Part 2 : The error analysis of the h and h-p versions. Tech. Note BN-1037 ; Part 3 : The adaptive h-p version, Tech. Note BN-1038, IPST, University of Maryland, College Park, 1985. To appear in Nume. Math. | Zbl 0731.73078 | Zbl 0614.65089

[14] B. Guo, I. Babuska, The h-p Version of the Finite Element Method. Part I : The basic approximation results. Part II : General results and applications. To appear in Comp. Mech. 1 (1986). | MR 1017747 | Zbl 0634.73058 | Zbl 0634.73059

[15] G. H. Hardy, T. E. Littlewood, G. Polya, Inequalities. Cambridge University Press, Cambridge, 1934. | JFM 60.0169.01 | Zbl 0010.10703

[16] V. A. Kondrat'Ev, Boundary value problems for elliptic equations in domains with conic or angular points. Trans. Moscow Math. Soc. (1967), 227-313. | MR 226187 | Zbl 0194.13405

|17] J. L. Lions, E. Magenes, Non-homogeneous boundary value problems and applications-I. Springer-Verlag, Berlin, Heidelberg, New York, 1972. | Zbl 0223.35039

[18] A. Pinkus, n-widths in Approximation Theory. Springer-Verlag, Berlin, Heidelberg, New York, Tokyo, 1985. | MR 774404 | Zbl 0551.41001

[19] E. M. Stein, Singular integrals and differentiability properties of functions. Princeton University Press, Princeton, N. J., 1970. | MR 290095 | Zbl 0207.13501

[20] G. Strang and G. J. Fix, An Analysis of the Finite Element Method. Prentice-Hall, Inglewood Cliffs, 1973. | MR 443377 | Zbl 0278.65116 | Zbl 0356.65096

[21] B. A. Szabo, PROBE : Theoretical Manual. Noetic Technologies Corporation, St Louis, Missouri, 1985.

[22] B. A. Szabo, Computation of Stress Field Parameters in Area of Steep stress gradients. Tech. Note WU/CCM-85/1, Center for Computational Mechanics, Washington University, 1985. | Zbl 0586.73170

[23] B. A. Szabo, Mesh Design of the p-Version of the Finite Element Method. Lecture at Joint ASME/ASCE Mechanics Conference, Albuquerque, New Mexico, June 24-26, 1985. Report WV/CCM-85/2, Center for Computational Mechanics, Washington University, St Louis. | Zbl 0587.73106

[24] B. A. Szabo, Implementation of a Finite Element Software System with h- and p-Extension Capabilities. Proc., 8th Invitational UFEM Symposium : Unification of Finite Element Software Systems. Ed. by H. Kardestuncer, The University of Connecticut, May 1985.