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The finite element solution of parabolic equations. (English) Zbl 0427.65075

MSC:
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations
65N15 Error bounds for boundary value problems involving PDEs
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References:
[1] P. G. Ciarlet, A. P. Raviart: The combined effect of curved boundaries and numerical integration in isoparametric finite element methods. In A. K. Aziz: The mathematical foundations of the finite element method with applications to partial differential equations. Academic Press. New York and London. 1972. · Zbl 0262.65070
[2] P. A. Raviart: The use of numerical integration in finite element methods for solving parabolic equations. Lecture presented at the Conference on Numerical Analysis. Royal Irish Academy. Dublin, August 14-18, 1972.
[3] Jindřich Nečas: Les Méthodes Directe en Théorie des Equations Elliptiques. Mason. Paris. 1967. · Zbl 1225.35003
[4] V. J. Smirnov: Kurs vyššej matěmatiki. tom V. Gosudarstvěnnoje izdatělstvo fiziko-matěmatičeskoj litěratury. Moskva. 1960.
[5] Miloš Zlámal: Finite Element Multistep Discretizations of Parabolic Boundary Value Problems. Mathematics of Computation, 29, Nr 130 (1975), 350-359. · doi:10.1090/S0025-5718-1975-0371105-2
[6] Miloš Zlámal: Curved Elements in the Finite Element Method I. SIAM J. Numer. Anal., 10. No 1 (1973), 229-240. · Zbl 0285.65067 · doi:10.1137/0710022
[7] Miloš Zlámal: Curved Elements in the Finite Element Methods II. SIAM J. Numer. Anal., 11. No 2 (1974), 347-362. · Zbl 0277.65064 · doi:10.1137/0711031
[8] Miloš Zlámal: Finite Element Methods for Parabolic Equations. Mathematics of Computation, 28, No 126 (1974), 393-404. · doi:10.1090/S0025-5718-1974-0388813-9
[9] T. Dupont G. Fairweather J. P. Johnson: Three-level Galerkin Methods for Parabolic Equations. SIAM J. Numer. Anal., 11, No 2 (1974). · Zbl 0313.65107 · doi:10.1137/0711034
[10] M. Lees: A priori estimates for the solutions of difference approximations to parabolic differential equations. Duke Math. J., 27 (1960), 287-311. · Zbl 0092.32803 · doi:10.1215/S0012-7094-60-02727-7
[11] Miloš Zlámal: Finite element methods for nonlinear parabolic equations. R.A.I.R.O. Analyse numérique/Numerical Analysis, 11, No 1 (1977), 93-107.
[12] W. Liniger: A criterion for A-stability of linear multistep integration formulae. Computing, 3 (1968), 280-285. · Zbl 0169.19902 · doi:10.1007/BF02235394
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