Superconvergence of the gradient of Galerkin approximations for elliptic problems

Mitsuhiro T. Nakao

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

  • Volume: 21, Issue: 4, page 679-695
  • ISSN: 0764-583X

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Nakao, Mitsuhiro T.. "Superconvergence of the gradient of Galerkin approximations for elliptic problems." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 21.4 (1987): 679-695. <http://eudml.org/doc/193520>.

@article{Nakao1987,
author = {Nakao, Mitsuhiro T.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {orthogonal polynomials},
language = {eng},
number = {4},
pages = {679-695},
publisher = {Dunod},
title = {Superconvergence of the gradient of Galerkin approximations for elliptic problems},
url = {http://eudml.org/doc/193520},
volume = {21},
year = {1987},
}

TY - JOUR
AU - Nakao, Mitsuhiro T.
TI - Superconvergence of the gradient of Galerkin approximations for elliptic problems
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1987
PB - Dunod
VL - 21
IS - 4
SP - 679
EP - 695
LA - eng
KW - orthogonal polynomials
UR - http://eudml.org/doc/193520
ER -

References

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  3. [3] M. BAKKER, One-dimensional Galerkin methods and superconvergenceatinterior nodal points, SIAM J. Numer. Anal. 21 (1984) 101-110. Zbl0571.65078MR731215
  4. [4] C. CHEN, Superconvergence of finite element solutions and its derivatives, Numerical Mathematics, 2 (1981), 118-125 (Chinese). Zbl0511.65080MR635547
  5. [5] J. F. CIAVALDINI & M. CROUZEIX, finite element method scheme for onedimensional elliptic équations with high super convergence at the node, , Numer.Math. 46 (1985) 417-427. Zbl0548.65067MR791699
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  7. [7] J. Jr. DOUGLAS T. DUPONT & M. F. WHEELER, An L°° estimate and asuperconvergence resuit for a Galerkin method for elliptic équations based ontensor products of pieeewise polynomials, RAIRO 8 (1974) 61-66. Zbl0315.65062MR359358
  8. [8] M. KRIZEK & P. NEITTAANMÀKI, Superconvergence phenomenon in the finite element method arising from averaging gradients, , Numer. Math. 45 (1984) 105-116. Zbl0575.65104MR761883
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  10. [10] N. LEVINE, Superconvergent recovery of the gradient from pieceewise linear finite-element approximations, IMA J. Numer. Anal. 5 (1985) 407-427. Zbl0584.65067MR816065
  11. [11] M. NAKAO, Some superconvergence estimates for a Galerkin method for elliptic problems, Bull. Kyushu Inst. Tech. (Math. Natur. Sci.), 31 (1984) 49-58. Zbl0575.65105MR763228
  12. [12] M. T. NAKAO, L error estimates and superconvergence results for a collocation- H - 1 -Galerkin method for elliptic equations, Memoirs of the Faculty of Science, Kyushu University, Ser. A, 39 (1985) 1-25. Zbl0584.65073MR783218
  13. [13] M. T. NAKAO, Some superconvergence of Galerkin approximations for parabolic and hyperbolic problems in one space dimension, Bull. Kyushu Inst. Tech. (Math. Natur. Sci.) 32 (1985) 1-14. Zbl0623.65119MR797452
  14. [14] M. T. NAKAO, Error estimates of a Galerkin method for some nonlinear Sobolev equations in one space dimension, Numer. Math. 47 (1985) 139-157. Zbl0575.65112MR797883
  15. [15] L. A. OGANESYAN and L. A. rUKHOVETS, Study of the rate of convergence of variational difference schemes for second order elliptic equations in a two dimensional field with a smooth boundary, USSR Comp. Math, and Math.hysics, 9 (1969) 158-183. Zbl0241.65073
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  18. [18] Q. Z H U, Uniform superconvergence estimates of derivatives for the finite elementmethod, Numerical Mathematics, 4 (1983) 311-318 (Chinese). Zbl0549.65073

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