Numerical analysis of nonlinear elliptic-parabolic equations

Maitre, Emmanuel

ESAIM: Modélisation mathématique et analyse numérique, Tome 36 (2002) no. 1, pp. 143-153.

This paper deals with the numerical approximation of mild solutions of elliptic-parabolic equations, relying on the existence results of Bénilan and Wittbold (1996). We introduce a new and simple algorithm based on Halpern's iteration for nonexpansive operators (Bauschke, 1996; Halpern, 1967; Lions, 1977), which is shown to be convergent in the degenerate case, and compare it with existing schemes (Jäger and Kačur, 1995; Kačur, 1999).

Classification : 65M12, 35K65, 35K55, 65N22
Mots clés : elliptic-parabolic, numerical, iterative method

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