Abstract
We consider a mixed boundary-value problem for a quasilinear elliptical equation of second order in the rectangle Ω with a generalized solution in W 21 (Ω). Exact difference scheme operators are applied to construct a first-order accurate difference scheme in the L2 grid norm.
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References
H. Gajewski, K. Groeger, and K. Zacharias, Nonlinear Operator Equations and Operator Differential Equations [Russian translation], Moscow (1978).
A. A. Samarskii, R. D. Lazarov, and V. L. Makarov, Difference Schemes for Differential Equations with Generalized Solutions [in Russian], Moscow (1987).
Ph. G. Ciarlet, The Finite Element Method for Elliptic Problems, North Holland, Amsterdam (1978).
Additional information
Kiev Technological Institute of Light Industry. Translated from Vychislitel'naya i Prikladnaya Matematika, No. 75, pp. 50–55, 1991.
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Voitsekhovskaya, T.G. Rate of convergence bound of difference schemes for quasilinear elliptical equations with solutions inW 12 . J Math Sci 72, 3086–3090 (1994). https://doi.org/10.1007/BF01259476
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DOI: https://doi.org/10.1007/BF01259476