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On a conjugate semi-variational method for parabolic equations. (English) Zbl 0278.35048


MSC:

35K20 Initial-boundary value problems for second-order parabolic equations
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35B45 A priori estimates in context of PDEs
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References:

[1] M. A. Biot: Thermoelasticity and irreversible thermodynamics. J. Appl. Phys. 27 (1956), 240-253. · Zbl 0071.41204
[2] R. A. Schapery : Irreversible thermodynamics and variational principles with applications to viscoelasticity. Aeronaut. Res. Labs. Wright-Patterson Air Force Base, Ohio (1962).
[3] J. Douglas Jr. T. Dupont: Galerkin methods for parabolic equations. SIAM J. Numer. Anal. 7 (1970), 4, 575-626. · Zbl 0224.35048
[4] I. Hlaváček: On a semi-variational method for parabolic equations. I. Aplikace matematiky 17 (1972), 5, 327-351, II. Aplikace matematiky 18 (1973), 1, 43-64.
[5] J. P. Aubin H. G. Burchard: Some aspects of the method of the hypercircle applied to elliptic variational problems. Numer. Sol. of Part. Dif. Eqs-II, Synspade 1970, 1 - 67.
[6] I. Hlaváček: Variational principles for parabolic equations. Aplikace matematiky 14 (1969), 4, 278-297. · Zbl 0182.13803
[7] J. L. Lions: Equations differentielles operationelles et problèmes aux limites. Grundlehren Math. Wiss., Bd 111, Springer 1961.
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