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Crouzeix, Michel

Une méthode multipas implicite-explicite pour l’approximation des équations d’évolution paraboliques. (French) Zbl 0419.65057

Numer. Math. 35, 257-276 (1980).
Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page
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Cited in 1 Review
Cited in 88 Documents

MSC:

65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
35G10 Initial value problems for linear higher-order PDEs
35K25 Higher-order parabolic equations

Keywords:

linear evolution equations; parabolic type; initial value problem; multistep methods; stability and convergence of difference methods
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Full Text: DOI EuDML

References:

[1] Bramble JH (1978) Conférence à l’école polytechnique de Paris
[2] Crouzeiz M, Raviart PA (1978) Approximation d’équations d’évolution linéaires par des méthodes multipas. (Rencontre IRIA Novosibirsk juin 1976, Etude Numérique des Grands Systèmes, Dunod. Paris.)
[3] Helfrich HP (1975) Lokale Konvergenz des Galerkinverfahrens bei Gleichungen vom parabolischen Typ in Hilberträumen, Doctoral dissertation, Freiburg
[4] Henrici P (1962) Discrete variable methods in ordinary differential equations, John Wiley, New York · Zbl 0112.34901
[5] Le Roux MN (1979) Semi-discrétisation en temps pour les équations d’évolution paraboliques lorsque l’opérateur dépend du temps, RAIRO 13:119-137 · Zbl 0413.65066
[6] Lions JL (1961) Equations différentielles opérationnelles, Springer, Berlin Heidelberg New York
[7] Lions PL, Mercier B (1978) Splitting algorithms for the sum of two non linear operators, Ecole Polytechnique, rapport interne n{\(\deg\)} 29 du centre de Mathématiques Appliquées
[8] Raviart PA (1972) The use of numerical integration in finite element methods for solving the parabolic equations. Topics in Numerical Analysis. Proceedings of the R.I.A.N.A. Academic Press, New York, p 233
[9] Steihaug T, Wolfbrandt A (1977) An attempt to avoid exact jacobian and non linear equations in the numerical solution of stiff differential equations, Goteborg report · Zbl 0451.65055
[10] Temam R (1968) Sur la stabilité et la convergence de la méthode des pas fractionnaires. Ann Mat Pura Appl 79:191-380 · Zbl 0174.45804 · doi:10.1007/BF02415183
[11] Zlámal M (1977) Finite element methods for non linear parabolic equations, RAIRO 11:93-107
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