Volume 36, Number 1, January/February 2002
|Page(s)||143 - 153|
|Published online||15 April 2002|
Numerical analysis of nonlinear elliptic-parabolic equations
Laboratoire de Mathématiques et Application, Université de Haute-Alsace, 4 rue des frères Lumière, 68093 Mulhouse Cedex, France. E.Maitre@univ-mulhouse.fr.
Revised: 16 November 2001
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).
Mathematics Subject Classification: 65M12 / 35K65 / 35K55 / 65N22
Key words: Elliptic-parabolic / numerical / iterative method.
© EDP Sciences, SMAI, 2002
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