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Hlaváček, Ivan
On a semi-variational method for parabolic equations. II. (English). Aplikace matematiky, vol. 18 (1973), issue 1, pp. 43-64
MSC: 65L05, 65M10, 65M99, 65N30 | MR 0323124 | Zbl 0253.65065 | DOI: 10.21136/AM.1973.103447
Summary:
The invariance of the $n$-th semivariational approximation with respect to the polynomial bases and its coincidence with the $n$-th Padé approximation at the basic time instants are proved for the case of the homogeneous abstract parabolic equation. The method and theorems are also extended to parabolic problems with inhomogeneous boundary conditions and to equations with two positive definite operators.
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On a semi-variational method for parabolic equations. I
References:
[1] I. Hlaváček: On a semi-variational method for parabolic equations I. Aplikace matematiky 17 (1972), 5, 327-351. MR 0314285
[2] A. Ralston: A first course in numerical analysis. Mc Graw-Hill, 1965. MR 0191070 | Zbl 0139.31603
[3] I. Hlaváček J. Nečas: On inequalities of Korn's type. Archive for Rational Mechanics and Analysis, 36, 4, 1970, 305-344. DOI 10.1007/BF00249518 | MR 0252844
[4] J. Nečas: Les méthodes directes en théorie des équations elliptiques. Prague, Academia 1967. MR 0227584
[5] J. Douglas, Jr. T. Dupont: Galerkin methods for parabolic equations. SIAM J. Numer. Anal. 7, 1970,4, 575-626. MR 0277126
[6] R. S. Vargа: Matrix iterative Analysis. Prentice-Hall, 1962. MR 0158502
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