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Discrete time Galerkin methods for a parabolic boundary value problem. (English) Zbl 0306.65073

MSC:
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
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[1] Bramble, J.; Nitsche, J. A., A generalized Ritz-least-squares method for Dirichlet problems, SIAM J. Numer. Anal., 10, 81-93 (1973) · Zbl 0287.65056
[2] Bramble, J. H.; Schatz, A. H., Rayleigh-Ritz-Galerkin methods for Dirichlet’s problem using subspaces without boundary conditions, Comm. Pure. Appl. Math., 23, 653-675 (1970) · Zbl 0204.11102
[3] Bramble, J.; Thomée, V., Semidiscrete-least squares method for a parabolic boundary value problem, Math. Comp., 26, 633-647 (1972) · Zbl 0268.65060
[4] Douglas, J.; Dupont, T., Galerkin methods for parabolic equations, SIAM J. Numer. Anal., 7, 575-626 (1970) · Zbl 0224.35048
[5] Nitsche, J. A., Linear Spline-Funktionen und die Methoden von Ritz für elliptische Randwertprobleme, Arch. Rational Mech. Anal., 36, 348-355 (1970) · Zbl 0192.44503
[6] Nitsche, J. A., Über ein Variationsprinzip zur Lösung von Dirichlet-Problemen bei Verwendung von Teilräumen, die keinen Randbedingungen unterworfen sind, Abh. Math. Sem. Univ. Hamburg, 36, 9-15 (1971) · Zbl 0229.65079
[7] Price, H. S.; Varga, R. S., Error bounds for semi-discrete Galerkin approximations of parabolic problems with application to petroleum reservoir mechanics, 74-94 (1970), R.I.: Numerical Solution of Field Problems in Continuum Physics, AMS Providence, R.I.
[8] Varga, R. S., Matrix Iterative Analysis (1962), Englewood Cliffs, N.J.: Prentice-Hall, Englewood Cliffs, N.J. · Zbl 0133.08602
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