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Zlamal, Milos

Finite element methods for nonlinear parabolic equations. (English) Zbl 0385.65049

RAIRO, Anal. Numér. 11, 93-107 (1977).
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Cited in 32 Documents

MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35K55 Nonlinear parabolic equations
35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
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\textit{M. Zlamal}, RAIRO, Anal. Numér. 11, 93--107 (1977; Zbl 0385.65049)
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References:

[1] 1. P. G. CIARLET and P. A. RAVIART, Interpolation Theory Over Curved Eléments, with Applications to Finite Element Methods. Computer Meth. Appl. Mech. Eng; Vol. 1, 1972, pp. 217-249. Zbl0261.65079 MR375801 · Zbl 0261.65079
[2] 2. P. G. CIARLET, Numerical Analysis of the Finite Element Method. Séminaire de Mathématiques Supérieures, Univ. de Montréal, 1975. Zbl0363.65083 MR495010 · Zbl 0363.65083
[3] 3. G. COMINI, S. DEL GUIDICE, R. W. LEWIS and O. C. ZIENKIEWICZ, Finite Element Solution of Non-Linear Heat Conduction Problems with Special Reference to Phase Change. Int. J. Numer. Meth. Eng., Vol. 8, 1974, pp. 613-624. Zbl0279.76045 · Zbl 0279.76045
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[6] 6. P. HENRICI, Discrete Variable Methods in Ordinary Differential Equations. Wiley, New York-London, 1962. Zbl0112.34901 MR135729 · Zbl 0112.34901
[7] 7. J. D. LAMBERT, Computational Methods in Ordinary Differential Equations.Wiley, London, 1972. Zbl0258.65069 MR423815 · Zbl 0258.65069
[8] 8. M. LEES, A priori Estimates for the Solutions of Difference Approximations to Parabolic Differential Equations. Duke Math. J., Vol. 27, 1960, pp. 287-311. Zbl0092.32803 MR121998 · Zbl 0092.32803
[9] 9. W. LINIGER, A Criterion for A-Stability of Linear Multistep Integration Formulae. Computing, Vol.3, 1968, pp. 280-285. Zbl0169.19902 MR239763 · Zbl 0169.19902
[10] 10. C. MIRANDA, Partial Differential Equations of Elliptic Type (second rev. edition). Springer, Berlin-Heidelberg-New York, 1970. Zbl0198.14101 MR284700 · Zbl 0198.14101
[11] 11. M. F. WHEELER, A priori L2 Error Estimates for Galerkin Approximations to Parabolic Partial Differential Equations. SIAM J. Numer. Anal., Vol. 10, 1973, pp. 723-759. Zbl0232.35060 MR351124 · Zbl 0232.35060
[12] 12. M. ZLAMAL, Curved Elements in the Finite Element Method I. SIAM J. Numer. Anal., Vol. 10, 1973, pp. 229-240. Zbl0285.65067 MR395263 · Zbl 0285.65067
[13] 13. M. ZLAMAL, Curved Elements in the Finite Element Method II. SIAM J. Numer. Anal., Vol. 11, 1974, pp. 347-362. Zbl0277.65064 MR343660 · Zbl 0277.65064
[14] 14. M. ZLAMAL, Finite Element Multistep Discretizations of Parabolic Boundary Value Problems. Mat. Comp., vol. 29, 1975, pp. 350-359. Zbl0302.65081 MR371105 · Zbl 0302.65081
[15] 15. M. ZLAMAL, Finite Element Methods in Heat Conduction Problems. To appear in The Mathematics of Finite Elements and Applications. MR451785
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