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


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
Full Text: EuDML


[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.
[6] Miloš Zlámal: Curved Elements in the Finite Element Method I. SIAM J. Numer. Anal., 10. No 1 (1973), 229-240. · Zbl 0285.65067
[7] Miloš Zlámal: Curved Elements in the Finite Element Methods II. SIAM J. Numer. Anal., 11. No 2 (1974), 347-362. · Zbl 0277.65064
[8] Miloš Zlámal: Finite Element Methods for Parabolic Equations. Mathematics of Computation, 28, No 126 (1974), 393-404.
[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
[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
[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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.