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

MSC:
65N30Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (BVP of PDE)
35K55Nonlinear parabolic equations
35K60Nonlinear initial value problems for linear parabolic equations
65N12Stability and convergence of numerical methods (BVP of PDE)
65M12Stability and convergence of numerical methods (IVP of PDE)
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Full Text: EuDML
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 · doi:10.1016/0045-7825(72)90006-0
[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 · doi:10.1002/nme.1620080314
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[5] 5. T. DUPONT, FAIRWEATHER G. and J. P. JOHNSON, Three-Level Galerkin Methods for Parabolic Equations. SIAM J. Numer. Anal; Vol. 11, 1974, pp. 392-410. Zbl0313.65107 MR403259 · Zbl 0313.65107 · doi:10.1137/0711034
[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 · doi:10.1215/S0012-7094-60-02727-7
[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 · doi:10.1007/BF02235394
[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 · doi:10.1137/0710062
[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 · doi:10.1137/0710022
[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 · doi:10.1137/0711031
[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 · doi:10.2307/2005556
[15] 15. M. ZLAMAL, Finite Element Methods in Heat Conduction Problems. To appear in The Mathematics of Finite Elements and Applications. MR451785