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Konvergenzaussagen für Projektionsverfahren bei linearen Operatoren. (German) Zbl 0336.65031


MSC:

65J05 General theory of numerical analysis in abstract spaces
65L10 Numerical solution of boundary value problems involving ordinary differential equations
65D30 Numerical integration
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References:

[1] Agmon, S.: Lectures on elliptic boundary value problems. Princeton: Van Nostrand 1965 · Zbl 0142.37401
[2] Agmon, S., Douglis, A., Nirenberg, N.: Estimates near the boundary of elliptic partial differential equations satisfying general boundary conditions. I. Comm. Pure Appl. Math.12, 623-727 (1959) · Zbl 0093.10401 · doi:10.1002/cpa.3160120405
[3] Amann, H.: Zum Galerkin-Verfahren für die Hammersteinsche Gleichung. Arch. Rat. Mech. Anal.35, 114-121 (1969) · Zbl 0186.20902 · doi:10.1007/BF00247615
[4] Aubin, J.-P.: Approximation of elliptic boundary value problems. New York: Wiley 1972 · Zbl 0248.65063
[5] Ciarlet, P. G.: An o(h 2) method for a non-smooth boundary value problem. Aequationes math.2, 39-49 (1968) · Zbl 0159.11703 · doi:10.1007/BF01833489
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[8] Collatz, L.: The numerical treatment of differential equations. Berlin: Springer 1960 · Zbl 0086.32601
[9] The mathematical foundations of the finite element method with applications to partial differential equations (A. K. Aziz, ed.), New York: Academic Press 1972
[10] Friedman, A.: Partial differential equations. New York: Holt, Rinehart, Winston 1969 · Zbl 0224.35002
[11] Kantorowitsch, L. W., Akilow, G. P.: Funktionalanalysis in normierten Räumen. Berlin: Akademie-Verlag 1964 · Zbl 0359.46017
[12] Krasnoselskij, M. A.: Topological methods in the theory of nonlinear integral equations. Oxford: Pergamon Press 1964
[13] Lucas, T. R., Reddien, G. W.: A high order projection method for nonlinear twopoint boundary value problems. Numer. Math.20, 257-270 (1973) · Zbl 0247.65050 · doi:10.1007/BF01407368
[14] Nitsche, J.: Vergleich der Konvergenzgeschwindigkeit des Ritzschen Verfahrens und der Fehlerquadratmethode. ZAMM49, 591-596 (1969) · Zbl 0221.65102 · doi:10.1002/zamm.19690491003
[15] Nitsche, J.: Zur Konvergenz von Näherungsverfahren bezüglich verschiedener Normen. Numer. Math.15, 224-228 (1970) · Zbl 0221.65092 · doi:10.1007/BF02168971
[16] Perrin, F. M., Price, H. S., Varga, R. S.: On higher-order numerical methods for nonlinear two-point boundary value problems. Numer. Math.13, 180-198 (1969) · Zbl 0183.44501 · doi:10.1007/BF02163236
[17] Petryshyn, W. V.: Projection methods in nonlinear numerical functional analysis. J. Math. Mech.17, 353-372 (1967) · Zbl 0162.20202
[18] Philipps, J. L.: The use of collocation as a projection method for solving linear operator equations. SIAM J. Numer. Anal.9, 12-28 (1972)
[19] Polskij, N. I.: Projective methods in applied mathematics. Sov. Math.3, 488-492 (1962) · Zbl 0209.47301
[20] Russel, R. D., Shampine, L. F.: A collocation method for boundary valueproblems. Numer. Math.19, 1-28 (1972) · Zbl 0221.65129 · doi:10.1007/BF01395926
[21] Schatz, A. H.: An observation concerning Ritz-Galerkin methods with indefinite bilinear forms. Math. Comp.28, 959-962 (1974) · Zbl 0321.65059 · doi:10.1090/S0025-5718-1974-0373326-0
[22] Shirali, S.: A note on Galerkin’s method for nonlinear equations. Aequations math.4, 198-200 (1970) · Zbl 0203.14802 · doi:10.1007/BF01817760
[23] Urabe, M.: Galerkin’s procedure for nonlinear periodic systems. Arch. Rat. Mech. Anal.20, 120-152 (1965) · Zbl 0133.35502 · doi:10.1007/BF00284614
[24] Vainikko, G. M.: On the stability and convergence of the collocation method. Differential Equations1, 186-194 (1965) · Zbl 0171.36503
[25] Witsch, K.: Konvergenzaussagen für Projektionsverfahren bei linearen Operatoren, insbesondere Randwertaufgaben. Dissertation, Köln (1974) · Zbl 0336.65031
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