Abstract
Finite element methods based on standard variational principle of minimum potential energy have been extensively studied from both practical and theoretical point of view. The mathematical theory of such methods is firmly established and is a part of the numerical analysis. In recent years, considerable efforts have been made to give a complete mathematical analysis of other finite element methods including mixed methods. All these works are related to the linear elleptic problems except that of Noor [1981a] which provides general ideas to obtain error estimates for the mixed finite element approximation of mildly nonlinear elliptic problems. It should be remarked that the nonlinear cases are much complicated, since each problem has almost to be treated individually. This is one of the reason that there is no unified and general technique to obtain the error estimates for the nonlinear problems. The mathematical model, we consider in this paper is highly nonlinear and has been the subject of recent investigations by many research workers including, Glowinski and Marroco [1975], Pelissier [1975], Noor [1981], Babuska [1976] and Bermudez and Moreno [1981].
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Noor, M.A., Elahi, K.Z., Noor, K.I. (1982). Mixed Finite Element Methods for Nonlinear Problems. In: Holz, K.P., Meissner, U., Zielke, W., Brebbia, C.A., Pinder, G., Gray, W. (eds) Finite Elements in Water Resources. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-02348-8_11
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DOI: https://doi.org/10.1007/978-3-662-02348-8_11
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