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Estimates for spline projections. (English) Zbl 0343.65045

MSC:
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65J05 General theory of numerical analysis in abstract spaces
65D05 Numerical interpolation
41A15 Spline approximation
41A25 Rate of convergence, degree of approximation
41A63 Multidimensional problems (should also be assigned at least one other classification number from Section 41-XX)
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References:
[1] 1. J.-P. AUBIN, Approximation des problèmes aux limites non homogènes et régularité de la convergence, Calcolo, Vol. 6, 1969, pp. 117-139. Zbl0201.12601 · Zbl 0201.12601 · doi:10.1007/BF02576128
[2] 2. I. BABUSKA, Approximation by Hill Functions, Comment. Math., Univ. Carolinae, Vol. 11, 1970, pp. 787-811. Zbl0215.46404 MR292309 · Zbl 0215.46404 · eudml:16399
[3] 3. I. BABUSKA, The Finite Element Method with Lagranian Multipliers, Numer. Math., vol. 20, 1973, pp. 179-192. Zbl0258.65108 MR359352 · Zbl 0258.65108 · doi:10.1007/BF01436561 · eudml:132183
[4] 4. I. BABUSKA, The Finite Element Method with Penalty, Math. Comp., Vol. 27, 1973, pp. 221-228. Zbl0299.65057 MR351118 · Zbl 0299.65057 · doi:10.2307/2005611
[5] 5. J. H. BRAMBLE and J. A. NITSCHE and A. H. SCHATZ, Maximum Norm Interior Estimates for Ritz Galerkin Methods, Math. Comp., vol. 29, 1976. Zbl0316.65023 MR398120 · Zbl 0316.65023 · doi:10.2307/2005279
[6] 6. J. H. BRAMBLE and J. E. OSBORN, Rate of Convergence Estimates for Non-Selfadjoint Eigenvalue Approximations, Math. Comp., Vol. 27, 1973, pp. 525-549. Zbl0305.65064 MR366029 · Zbl 0305.65064 · doi:10.2307/2005658
[7] 7. P. L. BUTZER and H. BERENS, Semi-Groups of Operators and Approximation, Die Grundlehren der math. Wissenschaften, Band 145, Springer-Verlag, New York, 1967. Zbl0164.43702 MR230022 · Zbl 0164.43702
[8] 8. C. DE BOOR and G. FIX, Spline Approximation by Quasi-Interpolants, J. Approximation Theory, vol. 8, 1973, pp. 19-45. Zbl0279.41008 MR340893 · Zbl 0279.41008 · doi:10.1016/0021-9045(73)90029-4
[9] 9. F. D. GUGLIELMO, Construction d’approximations des espaces de Sobolev sur des réseaux en simplexes, Calcolo, Vol. 6, 1969, pp. 279-331. Zbl0198.46206 MR433113 · Zbl 0198.46206 · doi:10.1007/BF02576159
[10] 10. G. FIX and G. STRANG, A Fourier Analysis of the Finite Element Method, Proc. CIME Conference, 1971, Cremonese, Rome (to appear). Zbl0356.65096 MR443377 · Zbl 0356.65096
[11] 11. J. T. KING, New Error Bounds for the Penalty Method and Extrapolation, Numer. Math., vol. 23, 1974, pp. 153-165. Zbl0272.65092 MR400742 · Zbl 0272.65092 · doi:10.1007/BF01459948 · eudml:132295
[12] 12. J. A. NITSCHE and A. H. SCHATZ, On Local Approximation Properties of of L 2 -projection on Spline-subspaces, Applicable Analysis, Vol. 2, No. 2, July 1972. Zbl0239.41007 · Zbl 0239.41007 · doi:10.1080/00036817208839035
[13] 13. J. A. NITSCHE, Interior Estimates for Ritz Galerkin Methods (preprint). · Zbl 0298.65071
[14] 14. I. J. SCHOENBERG, Approximation with Special Emphasis on Spline Functions, Academic Press, New York, London, 1969. Zbl0259.00010 MR251408 · Zbl 0259.00010
[15] 15. E. M. STEIN, Singular Integrals and Differentiability Properties of Functions, Princeton University Press, Princeton, New Jersey, 1970. Zbl0207.13501 MR290095 · Zbl 0207.13501
[16] 16. A. ZYGMUND, Trigonometrical Series, Vol. 2, Cambridge, England, 1959.
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