Geodesic
On the problem of superconvergence of finite element method algorithms
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 48 (2008) no. 12, pp. 2180-2185 Cet article a éte moissonné depuis la source Math-Net.Ru

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The coincidence of an approximate solution to the boundary value problem for an ordinary differential equation with the exact solution at mesh nodes is proved for a certain class of the generalized finite element methods. 
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A. A. Panin. On the problem of superconvergence of finite element method algorithms. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 48 (2008) no. 12, pp. 2180-2185. http://geodesic.mathdoc.fr/item/ZVMMF_2008_48_12_a9/

[1] Marchuk G. I., Agoshkov V. I., Vvedenie v proektsionno-setochnye metody, Nauka, M., 1981 | MR

[2] Syarle F., Metod konechnykh elementov dlya ellipticheskikh zadach, Mir, M., 1980 | MR

[3] Babuška I., Bauerjee U., Oshorn J. E., Superconvergence in the generalized finite element method, Techn. Rep. 0545, TICAM, Univ. Texas, Austin, Texas, 2004 http://www.ices.utexas.edu/media/reports/2005/0545.pdf

[4] Oganesyan L. A., Rukhovets L. A., “Issledovanie skorosti skhodimosti variatsionno-raznostnykh skhem dlya ellipticheskikh uravnenii vtorogo poryadka v dvumernoi oblasti s gladkoi granitsei”, Zh. vychisl. matem. i matem. fiz., 9:5 (1969), 1102–1120 | Zbl

[5] Babuška I. M., Sauter S. A., “Is the pollution effect of the FEM avoidable for the Helmholtz equation considering high wave numbers?”, SIAM J. Numer. Analys., 34:6 (1997), 2392–2423 | DOI | MR | Zbl

[6] Oden J. T., Prudhomme S., Demkowicz L., A posteriori error estimation for acoustic wave propagation problems, Techn. Rept 0432, TICAM, Univ. Texas, Austin, Texas, 2004 http://www.ices.utexas.edu/media/reports/2004/0432.pdf | MR

[7] Babuška I., Caloz G., Oshorn J., “Special finite element methods for a class of second order elliptic problems with rough coefficients”, SIAM J. Numer. Analys., 31:4 (1994), 945–981 | DOI | MR | Zbl

[8] Melenk J. M., On generalized finite element methods, PhD thesis, Univ. Maryland at College Park, 1995 http://www.math.tuwien.ac.at/~melenk/publications/diss.ps.gz

[9] Melenk J. M., Babuška I., “The partition of unity finite element method: Basic theory and applications”, Comput. Meth. Appl. Mech. Engng., 139:1–4 (1996), 289–314 | DOI | MR | Zbl

[10] Babuška I., Melenk J. M., “The partition of unity finite element method”, Int. J. Numer. Meth. Engng., 40:4 (1997), 727–758 | 3.0.CO;2-N class='badge bg-secondary rounded-pill ref-badge extid-badge'>DOI | MR | Zbl

[11] Nakao M. T., Hashimoto K., Watanahe Y., “A numerical method to verify the invertibility of linear elliptic operators with applications to nonlinear problems”, Computing, 75:1 (2005), 1–14 | DOI | MR | Zbl

[12] Nakao M. T., Hashimoto K., Constructive error estimates of finite element approximations for non-coercive elliptic problems and its applications, MHF Preprint Series, MHF 2007-5, Fac. Math. Kyushi Univ. Fukuoka, Japan, 12 pp.

[13] http://hdl.handle.net/2324/3405

[14] Mikhlin S. G., Pryamye metody v matematicheskoi fizike, Gostekhteorizdat, M., L., 1950

[15] Ladyzhenskaya O. A., Kraevye zadachi matematicheskoi fiziki, Nauka, M., 1973 | MR

[16] Nakao M. T., Yamamoto N., Kimura S., “On the best constant in the error bound for the $H_0^1$-projection into piecewise polynomial spaces”, J. Approx. Theory, 93:3 (1998), 491–500 | DOI | MR | Zbl

[17] Schultz M., Spline analysis, Prentice-Hall, London, 1973 | MR | Zbl

[18] Sauter S., “A refined finite element convergence theory for highly indefinite Helmholtz problems”, Computing, 78:2 (2006), 101–115 | DOI | MR | Zbl