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elliptic-parabolic

ESAIM: Mathematical Modelling and Numerical Analysis (1)

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Numerical analysis of nonlinear elliptic-parabolic equations
Emmanuel Maitre
Journal:

ESAIM: Mathematical Modelling and Numerical Analysis / Volume 36 / Issue 1 / January 2002

Published online by Cambridge University Press:

15 April 2002, pp. 143-153

Print publication:

January 2002
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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).