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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).
@article{M2AN_2002__36_1_143_0,
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/}
}
TY - JOUR AU - Maitre, Emmanuel TI - Numerical analysis of nonlinear elliptic-parabolic equations JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2002 SP - 143 EP - 153 VL - 36 IS - 1 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/m2an:2002006/ DO - 10.1051/m2an:2002006 LA - en ID - M2AN_2002__36_1_143_0 ER -
%0 Journal Article %A Maitre, Emmanuel %T Numerical analysis of nonlinear elliptic-parabolic equations %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2002 %P 143-153 %V 36 %N 1 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/m2an:2002006/ %R 10.1051/m2an:2002006 %G en %F M2AN_2002__36_1_143_0
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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