Application for Superconvergence of Finite Element Approximations for the Elliptic Problem by Global and Local L2-Projection Methods

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References

[1] J. Wang, “A Superconvergence Analysis for Finite Element Solutions by the Least-Squares Surface Fitting on Irregular Meshes for Smooth Problems,” Journal of Mathematical Study, Vol. 33, No. 3, 2000, pp. 229-243.

[2] R. E. Ewing, R. Lazarov and J. Wang, “Super-convergence of the Velocity along the Gauss Lines in Mixed Finite Element Methods,” SIAM Journal on Numerical Analysis, Vol. 28, No. 4, 1991, pp. 1015-1029.
doi:10.1137/0728054

[3] M. Zlamal, “Superconvergence and Reduced Integration in the Finite Element Method,” Mathematics Computation, Vol. 32, No. 143, 1977, pp. 663-685.
doi:10.2307/2006479

[4] L. B. Wahlbin, “Superconvergence in Galerkin Finite Element Methods,” Lecture Notes in Mathematics, Springer, Berlin, 1995.

[5] A. H. Schatz, I. H. Sloan and L. B. Wahlbin, “Superconvergence in Finite Element Methods and Meshes that Are Symmetric with Respect to a Point,” SIAM Journal on Numerical Analysis, Vol. 33, No. 2, 1996, pp. 505-521.
doi:10.1137/0733027

[6] M. Krizaek and P. Neittaanmaki, “Superconvergence Phenomenon in the Finite Element Method Arising from Avaraging Gradients,” Numerische Mathematik, Vol. 45, No. 1, 1984, pp. 105-116.

[7] J. Douglas and T. Dupont, “Superconvergence for Galerkin Methods for the Two-Point Boundary Problem via Local Projections,” Numerical Mathematics, Vol. 21, No. 3, 1973, pp. 270-278. doi:10.1007/BF01436631