The h - p version of the finite element method with quasiuniform meshes

I. Babuška; Manil Suri

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1987)

  • Volume: 21, Issue: 2, page 199-238
  • ISSN: 0764-583X

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Babuška, I., and 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 21.2 (1987): 199-238. <http://eudml.org/doc/193500>.

@article{Babuška1987,
author = {Babuška, I., Suri, Manil},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {h-p version of the finite element method; quasiuniform meshes; corner singularity; Error estimates; numerical example; plain strain elasticity problem; L-shaped domain; asymptotic},
language = {eng},
number = {2},
pages = {199-238},
publisher = {Dunod},
title = {The $h-p$ version of the finite element method with quasiuniform meshes},
url = {http://eudml.org/doc/193500},
volume = {21},
year = {1987},
}

TY - JOUR
AU - Babuška, I.
AU - Suri, Manil
TI - The $h-p$ version of the finite element method with quasiuniform meshes
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1987
PB - Dunod
VL - 21
IS - 2
SP - 199
EP - 238
LA - eng
KW - h-p version of the finite element method; quasiuniform meshes; corner singularity; Error estimates; numerical example; plain strain elasticity problem; L-shaped domain; asymptotic
UR - http://eudml.org/doc/193500
ER -

References

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  1. [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. Zbl0268.65052MR421106
  2. [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. Zbl0487.65058MR623044
  3. [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. [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. Zbl0487.65059
  5. [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. Zbl0637.65103
  6. [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. Zbl0487.65059MR615529
  7. [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. Zbl0498.65050MR648550
  8. [8] I. BERGH and J. LOFSTROM, Interpolation Spaces. Springer, Berlin, Heidelberg, New York, 1976. Zbl0344.46071
  9. [9] P. G. CIARLET, The Finite Element Method for Elliptic Problems. North-Holland, 1978. Zbl0383.65058MR520174
  10. [10] M. R. DORR, The approximation theory for the p-version of the finite element method. SIAM J. Numer. Anal. 21 (1984), 1180-1207. Zbl0572.65074MR765514
  11. [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. Zbl0617.65109MR821906
  12. [12] P. GRISVARD, Elliptic problems in nonsmooth domains. Pitman, Boston, 1985. Zbl0695.35060MR775683
  13. [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. 
  14. [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). Zbl0634.73059MR1017747
  15. [15] G. H. HARDY, T. E. LITTLEWOOD, G. POLYA, Inequalities. Cambridge University Press, Cambridge, 1934. Zbl0010.10703JFM60.0169.01
  16. [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. Zbl0194.13405MR226187
  17. |17] J. L. LIONS, E. MAGENES, Non-homogeneous boundary value problems and applications-I. Springer-Verlag, Berlin, Heidelberg, New York, 1972. Zbl0223.35039
  18. [18] A. PINKUS, n-widths in Approximation Theory. Springer-Verlag, Berlin, Heidelberg, New York, Tokyo, 1985. Zbl0551.41001MR774404
  19. [19] E. M. STEIN, Singular integrals and differentiability properties of functions. Princeton University Press, Princeton, N. J., 1970. Zbl0207.13501MR290095
  20. [20] G. STRANG and G. J. FIX, An Analysis of the Finite Element Method. Prentice-Hall, Inglewood Cliffs, 1973. Zbl0356.65096MR443377
  21. [21] B. A. SZABO, PROBE : Theoretical Manual. Noetic Technologies Corporation, St Louis, Missouri, 1985. 
  22. [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. Zbl0586.73170
  23. [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. Zbl0587.73106
  24. [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. 

Citations in EuDML Documents

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  1. Alexei Bespalov, Norbert Heuer, A new H(div)-conforming p-interpolation operator in two dimensions
  2. Alexei Bespalov, Norbert Heuer, A new (div)-conforming -interpolation operator in two dimensions
  3. Manil Suri, The p -version of the finite element method for elliptic equations of order 2 l
  4. Faker Ben Belgacem, Padmanabhan Seshaiyer, Manil Suri, Optimal convergence rates of h p mortar finite element methods for second-order elliptic problems
  5. Andrea Toselli, H P -finite element approximations on non-matching grids for partial differential equations with non-negative characteristic form
  6. Andrea Toselli, -finite element approximations on non-matching grids for partial differential equations with non-negative characteristic form
  7. Faker Ben Belgacem, Padmanabhan Seshaiyer, Manil Suri, Optimal convergence rates of mortar finite element methods for second-order elliptic problems
  8. Miloslav Vlasák, On polynomial robustness of flux reconstructions
  9. E. P. Stephan, M. Suri, The h - p version of the boundary element method on polygonal domains with quasiuniform meshes
  10. Christine Bernardi, Yvon Maday, Relèvement polynômial de traces et applications

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