no. 4
Superconvergence of the gradient of Galerkin approximations for elliptic problems
ESAIM: Modélisation mathématique et analyse numérique, Tome 21 (1987) no. 4, pp. 679-695 
@article{M2AN_1987__21_4_679_0,
     author = {Nakao, Mitsuhiro T.},
     title = {Superconvergence of the gradient of {Galerkin} approximations for elliptic problems},
     journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
     pages = {679--695},
     year = {1987},
     publisher = {AFCET - Gauthier-Villars},
     address = {Paris},
     volume = {21},
     number = {4},
     mrnumber = {921833},
     zbl = {0642.65073},
     language = {en},
     url = {https://www.numdam.org/item/M2AN_1987__21_4_679_0/}
}
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Nakao, Mitsuhiro T. Superconvergence of the gradient of Galerkin approximations for elliptic problems. ESAIM: Modélisation mathématique et analyse numérique, Tome 21 (1987) no. 4, pp. 679-695. https://www.numdam.org/item/M2AN_1987__21_4_679_0/

[1] R. A. Adams, Sobolev spaces, Academic Press (1975) | Zbl | MR

[2] M. Bakker, A note on C° Galerkin methods for two point boundary problems, Numer. Math. 38 (1982) 447-453. | Zbl | MR

[3] M. Bakker, One-dimensional Galerkin methods and superconvergenceatinterior nodal points, SIAM J. Numer. Anal. 21 (1984) 101-110. | Zbl | MR

[4] C. Chen, Superconvergence of finite element solutions and its derivatives, Numerical Mathematics, 2 (1981), 118-125 (Chinese). | Zbl | MR

[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. | Zbl | MR

[6] J. Jr. Douglas, & T. Dupont, Galerkin approximations for the two pointboundary problem using continuous pieeewise polynomial spaces, Numer. Math.22 (1974) 99-109. | Zbl | MR

[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. | Zbl | MR | Numdam

[8] M. Krizek & P. Neittaanmàki, Superconvergence phenomenon in the finite element method arising from averaging gradients, , Numer. Math. 45 (1984) 105-116. | Zbl | MR

[9] P. Lesaint & M. Zlâmal, Superconvergence of the gradient of finite element solutions, RAIRO Anal. Numer. 13 (1979), 139-166. | Zbl | MR | Numdam

[10] N. Levine, Superconvergent recovery of the gradient from pieceewise linear finite-element approximations, IMA J. Numer. Anal. 5 (1985) 407-427. | Zbl | MR

[11] M. Nakao, Some superconvergence estimates for a Galerkin method for elliptic problems, Bull. Kyushu Inst. Tech. (Math. Natur. Sci.), 31 (1984) 49-58. | Zbl | MR

[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. | Zbl | MR

[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. | Zbl | MR

[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. | Zbl | MR

[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. | Zbl

[16] R. Rannacher & R. Scott, Some optimal error estimates for piecewise linear finite element approximations, Math. Comp. 38 (1982) 437-445. | Zbl | MR

[17] A. H. Schatz, A weak discrete maximum principle and stability of the finite element method in L ∞ on plane polygonal domains I, Math. Comp. 34 (1980) 77-99. | Zbl | MR

[18] Q. Z H U, Uniform superconvergence estimates of derivatives for the finite elementmethod, Numerical Mathematics, 4 (1983) 311-318 (Chinese). | Zbl