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Dailey, J. W.; Pierce, J. G.

Error bounds for the Galerkin method applied to singular and nonsingular boundary value problems. (English) Zbl 0244.65075

Numer. Math. 19, 266-282 (1972).
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Cited in 9 Documents

MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
35J35 Variational methods for higher-order elliptic equations
35J40 Boundary value problems for higher-order elliptic equations
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\textit{J. W. Dailey} and \textit{J. G. Pierce}, Numer. Math. 19, 266--282 (1972; Zbl 0244.65075)
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References:

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[12] Jerome, J. W., Schumaker, L. L.: OnLg-splines. J. Approx. Theory2, 29-49 (1969). · Zbl 0172.34501 · doi:10.1016/0021-9045(69)90029-X
[13] Jerome, J. W., Varga, R. S.: Generalizations of spline functions and applications to nonlinear boundary value and eigenvalue problems. Theory and applications of spline functions (T. N. E. Greville, ed.), p. 103-155. New York: Academic Press 1969. · Zbl 0188.13004
[14] Kamke, E. A.: Über die definiten selbstadjungierten Eigenwertaufgaben bei gewöhnlichen linearen Differentialgleichungen. IV. Math. Z.48, 67-100 (1942). · JFM 68.0197.01 · doi:10.1007/BF01180005
[15] Nitsche, J.: Ein Kriterium für die Quasi-Optimalität des Ritzschen Verfahrens. Numer. Math.11, 346-348 (1968). · Zbl 0175.45801 · doi:10.1007/BF02166687
[16] Nitsche, J.: Verfahren von Ritz und Spline-Interpolation bei Sturm-Liouville-Randwertproblemen. Numer. Math.13, 260-265 (1969). · Zbl 0181.18204 · doi:10.1007/BF02167557
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[18] Pierce, J. G., Varga, R. S.: Higher order convergence results for the Rayleigh-Ritz method applied to eigenvalue problems. II. Improved error bounds for eigenfunctions (to appear). · Zbl 0223.65080
[19] Schultz, M. H.: Multivariate spline functions and elliptic problems, approximation with special emphasis on spline functions (ed. I. J. Schoenberg), p. 279-347. New York: Academic Press 1969.
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[25] Yosida, K.: Functional analysis. New York: Academic Press 1965. · Zbl 0126.11504
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