Geodesic
Numerical analysis of nonlinear elliptic-parabolic equations
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 36 (2002) no. 1, pp. 143-153

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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).

DOI : 10.1051/m2an:2002006
Classification : 65M12, 35K65, 35K55, 65N22
Keywords: elliptic-parabolic, numerical, iterative method 
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     author = {Maitre, Emmanuel},
     title = {Numerical analysis of nonlinear elliptic-parabolic equations},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {143--153},
     publisher = {EDP-Sciences},
     volume = {36},
     number = {1},
     year = {2002},
     doi = {10.1051/m2an:2002006},
     mrnumber = {1916296},
     zbl = {0998.65089},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an:2002006/}
}
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Maitre, Emmanuel. Numerical analysis of nonlinear elliptic-parabolic equations. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 36 (2002) no. 1, pp. 143-153. doi: 10.1051/m2an:2002006

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