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Fehlerabschätzungen für das Galerkinverfahren zur Lösung von Evolutionsgleichungen. (German) Zbl 0323.65037

MSC:
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65J05 General theory of numerical analysis in abstract spaces
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
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References:
[1] BABUSKA, I., AZIZ, A.K.: Survey lectures on the mathematical foundations of finite element method. Chapt.11 (with G.FIX). In: The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations. Part I. Ed. K. Aziz. Academic Press, New York, London (1972)
[2] DOUGLAS, Jr. J., DUPONT, T.: Galerkin methods for parabolic equations with nonlinear boundary conditions. Numer. Math.20, 213-237 (1973) · Zbl 0234.65096
[3] FIX, G., NASSIF, N.: On finite element approximation to time dependent problems. Numer. Math.19, 127-135 (1972) · Zbl 0244.65063
[4] KATO, T.: Perturbation Theory for Linear Operators. Springer Verlag, Berlin-Heidelberg-New York (1966) · Zbl 0148.12601
[5] KEEIN, S.G.: Linear differential equations in Banach spaces. Translations of Mathematical Monographs, Vol.29. American Mathematical Sociaty, Providence (1971)
[6] NITSCHE, J.: Vergleich der Konvergenzgeschwindigkeit des Ritzschen Verfahrens und der Fehlerquadratmethode. Z.Angew.Mech.49, 591-596 (1969) · Zbl 0221.65102
[7] NITSCHE, J.: Ein Kriterium für die Quasioptimalität des Ritzschen Verfahrens. Numer. Math.11, 346-348 (1968) · Zbl 0175.45801
[8] PEETRE, J., THOMÉE, V.: On the rate of convergence for discrete initial value problems. Chalmers Institute of Technology and the University of Göteborg, Department of Mathematics, No. 1967-1 (1967)
[9] PLEHWE, A.v.: Über das Galerkinverfahren zur genäherten Lösung von Anfangswertproblemen für Differentialgleichungen erster Ordnung im Hilbertraum. Inaugural Dissertation. Albert-Ludwigs-Universität, Freiburg i.Br., (1970)
[10] SOBOLEVSKII, P.E.: Approximate methods of solving differential equations in Banach spaces (Russian). Dokl. Akad. Nauk SSR115, 240-243 (1957), MR 20 # 1050
[11] SOBOLEVSKII, P.E.: Equations of a parabolic type in a Banach space. Trudy Moscov Math. Soc. Ob??.10, 297-350 (1961). American Math. Soc. Transl. (2)49, 1-62 (1966)
[12] SOBOLEVSKII, P.E.: The Bubnov-Galerkin method for parabolic equations in Hilbert space. Soviet Math. Doklady9, 154-157 (1968)
[13] STRANG, G., FIX, G.J.: An Analysis of the Finite Element Method. Prentice-Hall, Inc. Englewood Cliffs, N.J. (1973) · Zbl 0356.65096
[14] TANABE, H.: A class of equations of evolution in a Banach space. Osaka Math. J.11, 121-145 (1959) · Zbl 0098.31201
[15] THOMÉE, V.: Spline approximation and difference schemes for the heat equation. The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations. Ed. K. Aziz. Academic Press, New York-London (1972)
[16] THOMÉE, V.: Some convergence results for Galerkin methods for parabolic boundary value problems. Chalmers University of Technology and the University of Göteborg, Department of Mathematics, No. 1974-3 (1974)
[17] WHEELER, M.F.: A priori L2 error estimates for Galerkin approximations to parabolic partial differential equations. SIAM J. Numer. Anal.10, 723-759 (1971) · Zbl 0258.35041
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